“What is it with Legionella and U.S. veterans?”
Legionella bacteria thrives in old, poorly maintained air conditioning systems, and VA hospitals are, for the most part, old and poorly maintained.
http://www.mayoclinic.org/diseases-conditions/legionnaires-disease/basics/causes/con-20028867
But you are right, a VA HVAC system would be perfect for growing Legionella.