A cop can do any damn thing he wants to you, and arrest/charge you with any damn thing he wants. Whether it will hold up in court is an entirely different matter. The charges may get thrown out, he may be reprimanded/spanked/fired/whatever, but he CAN cause you mucho grief and expense whether it's justified or not. BTDT.
Personally, I'll be as cooperative and honest as possible, but I will be VERY guarded as to what I say, and will certainly request legal counsel first. Refusing to speak will surely piss them off and inflame the situation. I'll demand my rights, but not to the point of getting tazed and clubbed for it.