***** NOT A TEACHER *****
Why it doesn't work with pretend?
Are there special words don't work with as is?
May I just add a few words to Mr. Bailey's excellent comments?
I believe that these sentences are also possible:
1. He acts as if he was/were wise, but he isn't. ( Americans would greatly appreciate your using the subjunctive "were.")
2. He acted
as if he was wise, but he wasn't. (In older English, the subjunctive was also used here. But today, most
teachers suggest using the subjunctive only for present or future statements.)