Does it? Think about it. Look at how many shots we give our infants the first year of their lives. I think we would have noticed by now if their infection rate was high.
Some people will have idiosyncratic reactions to many things that enter their bodies. A guy eats a strawberry one day and dies. This maybe a part of what is happening.
The smallpox vaccine is basically the one we received in the 40's and 50's. We already know some will react badly. The anthrax is newer but I know for a fact this was totally, TOTALLY approved by the FDA and although many complain that the FDA is a bunch a liberal bureaucratic neurotics (which they are), the vaccine has been shown to be safe, well at least as safe as driving in a car.
There are always risks and benefits to a decision. Hard pressed there is a government conspiracy to risk a vaccination, under today's scrutiny, to a threat we don't even know will happen.
As a side note: I was at Dover AFB when some of our men and women were coming home. (That was so great to see!) They actually were a bit surprised at the size of their smallpox vaccine scar, until I showed them mine.