Yes, the broker can restrain you from exercising your puts. Schwab would have done this to my PUDA puts from that account if they had not been able to find shares to borrow (at a 55% yearly interest rate) 1 hour before expiration. Sadly the puts on that account were the $9 strike puts, so I had to exercise.
I even called the Options council and they verified that brokers have the right to refuse the put-exercise if it would make them violate short-sale SEC rules (ie: no naked shorting).
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