Again, don't you think a policeman has the power to arrest somebody who acts tumultuous during a police investigation?
The police did not arrest Gates for his behavior during their investigation. If they had, they would have charged him with impeding an investigation. The police arrested Gates for spouting off his crackpot opinions after they had determined he lived there.
The police clearly had the power to arrest Gates for spouting off his crackpot ideas. And thus we do not live in a free society. What you really need to do is read Taranto’s comments on this beginning with:
http://online.wsj.com/public/article/SB10001424052970203946904574302304074459422.html
sub-entitled “Henry Louis Gates is not a burglar. Neither is James Taranto.”