I thought the body triangle was just used to keep someone from turning back into you once you've mounted their back. I've had tight body triangles thrown on me as a set up for RNC but nothing I would tap to or even complain about and I just kept fighting. The person throwing on the body triangle wasn't trying to dick with me, they were just trying to keep me from turning around, and that takes a lot of pressure. Complaining about the pressure of a body triangle is like complaining about body pressure during side amount (although admittedly I "lighten up" side mount pressure when we are doing a LOT of side mount drilling). But maybe your taining partner has a big stomach or something.
On the other hand I almost tapped last night from a very forceful crossface which managed to hit my "pinched nerve" or whatever has been going on, on that side of my neck, so I know that sometimes pretty common moves can create unusual distress for some training partners. But I didn't tap to the crossface and I didn't complain about it later either (I had a kind training partner who ramped up the pressure gradually, instead of torquing it on in an instant).
On the other hand I once had a training partner tap to a cross face I was applying to him, not because he was a wuss but because I wasn't going anywhere out of the side mount and since we were just stalemated it seemed pointless - after a while - to just hang out and suffer.
Basically I think you should complain about someone that doesn't let up when you tap, but otherwise sometimes discomfort is part of the game.