There are more obscure idioms to lose less sleep over, I think. ;) Perhaps it's because a trivet is basically stable? Really, who knows.

I think you mean right as a rivet not trivet :) This is a rivet by the way http://t1.gstatic.com/images?q=tbn:ANd9GcR3bl-5ZwrlqapgJCMiThIVaRugYQBnBR2g1wk7x0TCrIXqvyDO The meaning originally means it is right just as a rivet is straight. A rivet is always the same, and it never changes. So it does mean "quite" or "really" right whatever adverb you want :) Cheers!