Your *other* theory is neat, but it doesn't explain why the AMI building failed to get the same sort of threatening notes that the actual anthrax targets received.
On the other hand, a cross-contaminated rent check explains it easily; there was no threatening note to AMI...because it wasn't the intended target. This fact also explains why no one is sure *which* letter to AMI was the anthrax carrier. It *might* have been the J-Lo letter, but that letter was so insignificant to the editors that it was discarded; something that can hardly be said for the actual Greendale School return address letters to the real targets.
Occam's Razor. The terrorists had to pay their apartment rent. Anthrax spores are so small that they filter through paper envelopes as well as attach themselves to paper objects such as cash and checks (e.g. rent payment checks). The terrorists' landlord frequented her husband's AMI building. Two people at the AMI building contracted anthrax.