Bayesian credible intervals: "superiority" even if 1 is included? In a recent medical publication comparing a cardiac device to anticoagulation ("blood thinners") using a Bayesian statistical model to evaluate the efficacy of preventing strokes and cardiovascular death, the rate ratio (RR) of the primary outcome (stroke and death and all that) was 0.60 with a 95% credible interval of 0.41-1.05, and the posterior probability of superiority was stated to be 96%.
So my question is: how can the posterior probability of superiority (i.e., the device is better than anticoagulation) be 96% if the 95% credible interval of the RR includes 1, meaning it includes the possibility that the device is not better? As I have understood the Bayesian 95% credible interval so far, it answers the question "give me an interval in which the true value of the statistic lies with a probability of 95%", in this case stretching from above 1 to below 1; so how can I still be 96% certain that it is below 1? 
Is this a plain mistake, or is there a trick to Bayesian statistics that eludes my admittedly poor understanding of these things?
Link (PubMed) to the trial publication: http://www.ncbi.nlm.nih.gov/pubmed/25399274
 A: I try to provide intuition for why the situation reported in the question is not a contradiction by considering a couple  of examples where this situation (as I understand it). In the end, I also point out what actually could be deduced about possible credible intervals based on the 96% probability.
A discrete dice example
Consider a fair 6-sided die. The result is below $5$ with probability $2/3$ but still the probability of obtaining a result in the set $\{4,5,6\}$, that contains $5$, is $1/2$ - below $2/3$!
A continuous example talking about credible intervals and exceeding $1$
Suppose the posterior distribution for $\theta$  is uniform in the interval $[0.04, 1.04]$,
\begin{equation}
\theta \mid \textrm{Data} \sim U(0.04, 1.04).
\end{equation}
Then, we have 
\begin{equation}
P(\theta < 1 \mid \textrm{Data}) = 0.96.
\end{equation}
However,
\begin{equation}
P(\theta \in [0.065, 1.015]) = 0.95 
\end{equation}
So $[0.065, 1.015]$ is a 95% credible interval (even a central one).
A more absurd example
If the credible interval  is not required to be central, we get arbitrarily small "credibilities" by considering say $P(\theta\in [1-\epsilon, 1+\epsilon])$. 
What can instead be deduced from the 96% probability of superiority
$P(\theta < 1 \mid \textrm{Data}) = 0.96$ implies that any interval with posterior probability over 96% must contain values exceeding 1 (intuition: there is not enough probability mass below $1$). And that any interval with posterior probability over 4% must contain values below 1.
