I had a patient once who's cx was lacerated by our midwife. I don't know how--she does have long nails though (and a rough exam).
The poor woman started to hemorrhage. L&D nurses and docs told us she must have been pushing--weren't we telling her not to? Didn't we know she wasn't dilated? This is why only L&D nurses should be with laboring Pts.
Let me tell you, I was with this woman ALL DAY (she was my only Pt, and a young, scared, non-english speaker), and this poor thing didn't give so much as a grunty push. Nada. There was no bleeding....midwife examines, 15 seconds later, small puddle in the bed...take her down....pretty large lac visualized. But nah, it was because she was pushing so hard on a closed cervix.
So, yeah, I think it's possible.