They already deal with that sort of thing from students disgruntled with their grades anyway, I don't see the risk at all. In Canada I think there's a common practice of students asking to see their letters- I haven't done it but I think it would be seen as weird or suspicious for a prof to refuse. If profs are straight up lying about their students then I think students would be justifiably angry, and should therefore have a right to see them in any case. Clearly the more at-risk party here is the students due to the power differential (and the lack of, y'know, six-figure income and tenure).