I don't see any reason to believe this. It could be as simple as going out into the middle of a field or a wood on a windless day and tipping a prepared pouch into the envelope. Any small amounts of anthrax which escaped would be so diluted by the time humans came into contact with them as to be harmless. As with anything elese, the dose is the poison. The preparers could have protected themselves in whole or in part by using antibiotics, or they could have been prepared immediately before the preparers ploughed hijacked jumbo jets into the WTC.
OTOH, some or all of the letters might very well have been pre-prepared abroad. It seems like a rather inconsequential issue to me. There are an infinite number of exact scenarios for how this was perpetrated. Why does it matter?
The question of whether the donor retains total control
over the supply of the Daschle anthrax is of some importance.