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It’s a possibility so worth checking. I had a cannondale that the previous owner had been using with a 30.9mm post. Having bought one myself, it was slipping. Realised it had been over tightened. I had to prize it open a bit because it wasn’t having any of the 31.6mm post I had. Worked eventually though and no more slipping, didn’t have to force it in after I’d spread the opening...
If it’s been over tightened or used with a post too small then the opening of the seat tube will indeed be too small for a 27.2 but that’s not to say that further down it isn’t.
Check the split in the tube at the back and make sure both sides of it are straight.