Okay hear me out here.
1. Moriarty would not have just been sending letters, he would be trying to gather a force of thugs
2. The grammar mistakes and other things like that on the teachers site would draw attention away from the smartest of the Cabal
3. In some stories Moriarty was a learned man who would give lectures at some places. Teacher isn't too far of a jump.
4. If someone were gathering a massive force of evil who else but him?
Implications
1. Moriarty has outgambited Mr. A by making his site look not correct.
2. Any number of normal people around fictionals could be part of the anti-fictional force. The cops that caught Peter, Don Juans fiance could be a sleeper agent ready to kill him if needed. The girls Adam was dating could have been taken out by agents in the restaurant(in order to convince him the Cabal could solve his problems, that way he is close in case of a need to take him out)