Correct way to interpret odds ratio I'm looking at a table of logistic regression results. Specifically, the table shows "Logistic regression model of hypertension status in relation to lead biomarkers in the normative aging study, Stratified by calcium intake". 
The outcome variable is the presence of hypertension (1-yes, 0-no).
The covariates are: age>=70 (1/0), family history of hypertension (1/0), ever smoker (1/0), BMI (kg/m^2), blood lead, tibia bone lead levels, and patella bone levels. 
The results are stratified by calcium intake (Low calcium intake, and High Calcium intake).
My question is really a more simple, basic one: Why is it not the same to say the following two things:
(a) "odds of hypertension are 3 times higher in males aged>=70 WITH a family history of hypertension versus males <70 years without a family history of hypertension, adjusted for the other variables"
(b) "odds of hypertension are 3 times higher in males aged<70 WITHOUT a family history of hypertension versus males aged>=70 WITH a family history of hypertension, adjusted for the other variables"?
Please let me know if I can be clearer, and thanks so much in advance!  A snapshot of the table is below:
 A: The problem you are discussing appears to be establishing the baseline for which your coefficients are deviating from.  There are four models in the output you provided (each stratified); let's assume we are dealing with model A with low calcium intake for this exercise
From the table you provided, it appears that No History (of family hypertension) and <70 years old represent the baselines.
Statement A suggests the following relationship concerning odds ratios.  Notice the coefficients in the table you provided support this interpretation ($1.29*2.34 = 3.0$)

Statement B suggests that hypertension is higher among men who are <70 with No History (of family hypertension).  

Statement B doesn't seem right and would be hard to support from the table you provided.  
A: The explanations would be equivalent if you replaced HIGHER with LOWER in either case. I'm assuming the odds are generally higher among older men with a family history, making statement a) the correct(er) one. The exposures in the comparison and referent group are inverted in either statement.
