So I guess you rehearsed the set at a tempo which was accepted as OK by everyone? If the drummer has been unilaterally pushing the tempos up a notch or two he has an "issue" which should be fixed. He's in the wrong and if someone (you) reminds him that every thing's too fast he can't complain.
Is your drummer saying that problems can't be discussed on a gig? The drummer on my gig last night had a go at the band after about 3 numbers for being too loud. We were and there was no argument, we all turned down. If this guy can't handle a simple change on the fly like playing a number slower he should be ashamed.
I don't agree with the "rehearse songs slower, because the drummer always plays them faster on the gig", idea. Rehearse the songs the way you want to gig them. Then play them exactly the same on the gig. That's what you rehearsed. . . that's what you intended, so don't play something different on the gig, just because one of the band doesn't/can't follow the script.