Camera definitely matters, as the problems with film-flatness from being left in the camera stem from the film being bent around a roller and holding that shape (hence it'll be the second shot after you've left it for a while that won't be flat.
I can't comment on the ones that you've mentioned, but in general it's the 'back' cameras that have the problem (mamiya 645 and hassy I can vouch for) where they're bent around rollers before being exposed.
The 'big SLR' style cameras (I can vouch for Pentacon6, but it should also apply to mamiya 6 and pentax 67 styles) take the film straight off the roll, past the shutter, then straight onto the take-up spool. Same goes for 35mm cameras, it's straight out of the cartridge past the shutter, no bending.
I've no idea about TLRs because I don't have one, but if you've got one just look to see if the film bends before going past the shutter.
The only 35mm cameras that might have a problem are weird ones, like 35mm TLRs or the Rollei 3000 (I don't have one, but I'm assuming that it bends film by the nature of its having a film back).