Confidence interval and probability - where is the error in this statement? If someone makes a statement like below:

"Overall, nonsmokers exposed to environmental smoke had a relative
risk of coronary heart disease of 1.25 (95 percent confidence
interval, 1.17 to 1.32) as compared with nonsmokers not exposed to
smoke."
What is the relative risk for the population as a whole? How many things are connected with coronary heart disease?
Of the vast
number of things that can be tested, very few actually are connected
to coronary heart disease, so the chance that any particular thing
chosen at random is connected is vanishingly small. Thus we can say
that the relative risk
for the population is 1. But the quoted interval does not contain the
value 1. So either there actually is a connection between the two
things, the probability of which is vanishingly small, or this is one
of the 5% of intervals that do not contain the parameter. As the
latter is far more likely than the former it is what we should assume. Therefore, the appropriate
conclusion is that the data set was almost certainly atypical of the
population, and thus no connection can be implied.
Of course, if there is some basis for assuming that more than 5% of
things are linked to coronary heart disease then there might be some
evidence in the statistic to support the suggestion that environmental
smoke is one of them. Common sense suggests that this is unlikely.

What is the error in their reasoning (as all health organizations agree that there is significant literature regarding the damaging effects of second-hand smoking)? Is it because of their premise that "Of the vast number of things that can be tested, very few actually are connected to coronary heart disease"? This sentence may be true for any randomly chosen factor (ie. how many dogs a person owns with the risk of coronary artery disease) but the a priori probability is much higher for second hand smoking and coronary heart disease than just 'any random factor'.
Is this the correct reasoning? Or is there something else?
 A: This is a quite interesting philosophical issue related to hypothesis testing (and thus in the frequentist setting also confidence intervals, as I explain here).
There are, of course, a lot of hypotheses that could be investigated - passive smoking causes coronary heart disease, drinking alcohol causes chd,  owning dogs causes chd, being a Capricorn causes chd...
If we choose one of all of these hypotheses at random, the probability of us choosing a hypothesis that happens to be true is virtually zero. This seems to be the argument in the quoted text - that it is very unlikely that we happened to test a true hypothesis.
But the hypothesis was not chosen at random. It was motivated by previous epidemiological and medical knowledge about coronary heart disease. There are theoretical mechanisms that explain how smoking could cause coronary heart disease, so it does not seem far-fetched to think that those would work for passive smoking as well.
The criticism in the quote may be valid for exploratory studies where a data set is mined for hypotheses. That is the reason that we don't accept such "discoveries" as facts - instead we require that the results can be replicated in new studies. Either way, the paper cited in the quote is a meta study and is therefore not affected by this problem.
We have seen empirically over the last centuries that testing hypotheses motivated by theory by comparing the predicted results to the observed results works. The fact that we believe in this procedure is the reason that we have made so much progress in medicine, engineering and science. It is the reason that I can write this on my computer and that you can read it on yours. To argue that this procedure is wrong is to argue that the scientific method is fundamentally flawed - and we have plenty of evidence that says otherwise.
I doubt that there is anything that a person who isn't willing to accept this kind of evidence actually will accept...
A: I really don't get why the author says that the probability of relative risk of coronary heart disease being 1 could be vanishingly small basing his analysis solely on a Confidence Interval; this is plain wrong. To me, it looks like he's using a frequentist setting, but he is reasoning bayesianly (which is pretty common). 
The only thing linked to a C.I. are classical significance tests but, as we all know, if $H_0:$ { There is no link between second hand smoking and coronary heart disease }, they give you $p(D_e|H_0)$ (where $D_e$ denotes "data at least as extreme as what we observed"), not $p(H_0|D)$ (where $D$ is the data), which is what he claims, and what is linked exactly to what you point out; you have to incorporate prior knowledge about that particular link! This comes from the fact that:
$$p(H_0|D)\propto p(D|H_0)p(H_0),$$
by Bayes Theorem, where $p(H_0)$ is the prior probability on $H_0$. 
A: While there is something to this Bayesian line of reasoning (deconstructed very thoroughly by Erik!), and indeed this line of thought would explain why many medical findings cannot be reproduced, this particular argument applies that thinking like a sledgehammer. 
The author presupposes two things without providing evidence: that exposure to smoke was chosen at random, and that almost nothing in the world causes heart disease. Under these lax standards of reasoning, the author could reject ANY conclusion that something causes heart disease. All you would need to do is assert:


*

*That the hypothesis was chosen at random, and

*That heart disease has very close to zero causes.


Both of these assertions are debatable (and, based on my general knowledge, very likely false). But, with these assumptions in place, even observing that 100% of people exposed to secondhand smoke dropped dead of a heart attack within a year, you could assert that the connection is merely a coincidental correlation with the hidden, singular, "true" cause.
A: There are many things wrong here. As @Néstor explains, he implicitly assumes prior probabilities on $H_0$ (no link) and $H_1$ (link). 
He places a very high weight (very close to 1) on $H_0$ and a very small weight on $H_1$. This is the first dubious thing he does, since there is a mechanistic link between smoke and heart disease (consider active smokers), the question really is if the exposure is enough. This does not even consider the previous studies done. So it's really not one of a "vast number of things" to be tested as wearing red socks for example would be. This means he already starts with a highly biased and not really justifiable prior.
He then updates his prior by stating that the probability of getting an 95%-confidence interval of not containing the true value has a probability of 5%. While this is true, this is not the chance of getting that particular interval under the assumption of the null hypothesis. Note that he would have treated a confidence interval of [1.17, 1.32] exactly the same as a confidence interval of [100, 200] which is clearly problematic. 
This is really important to the Bayesian approach: while you have a total probability of 5% of not getting an interval containing the 1 under the assumption that 1 is zero, the probability density of getting that particular interval is different (and smaller). 
The third mistake is that he never specified his prior nor states how likely $H_0$ has to be versus $H_1$ for him to get that result. It's just "vanishingly small". 
The fourth mistake is to say that the appropriate action to take would be to dismiss the data. Note that his result does not even depend on the data, his argument implies exactly the same action would have been done for any data at all. If you find an interesting link but suspect it might just be a fluke, the proper scientific thing to do is to try to replicate your result! 
A: I don't see anything obviously wrong with the paragraph in quotations, but I haven't seen the data and cannot check is numbers.  However, the two paragraphs that follow it are very unclear.
Suppose he had said, "Overall, nonsmokers who were morbidly obese had a relative risk of coronary heart disease of 1.25 (95 percent confidence interval, 1.17 to 1.32) as compared with nonsmokers who had normal body weight."  Would anyone have reason to doubt him?
