In my experience, PIs hire postdocs depending on a personal recommendations rather than anything else. And if they don't have it, they look on papers and they quality, for whom they worked, his whole history etc. Expertise matters only when you want them to start on a rather advanced topic and you require him to have for example a long experience with cell cultures, because they are going to cultivate something difficult.
I thing it doesn't matters if the institution has a "lower" limit than other. As I said, the PhDs are not the same, even from the same institutions.
My boss for example, has personal requirements higher than the faculty has. He wants his students to have a really good paper to finish (even if it means taking longer time to finish) even if the faculty would suffice with "just" any impact.
I don't thing it differs much across any profession. You may have a "qualified" plummer and he's a disaster, you may have a plummer who studied the same school and he's great. If the goverment pushes to have more graduates and more university degree holders (as my does), then logically the quality falls a bit. But not of all, the good will always be good. You just can't tell only from having some title, as, actually, you never did anyway, now there is just more of them. Don't thing it's anything new or anything "now it will be all worthless". Yes, the titles hold less prestige when everyone has it (and not everyone can be outstanding) but it's just titles. It doesn't mean the good students will be worse, maybe even oposite, they would want to stand out of the "crowd".
Apart from a society's influenced fluctuation of titles numbers I don't see much of a difference here. Any institution that keeps incompetent people with titles, just because titles, deserves the result. The other will select the "good" from the "bad" simply because they do good work or don't. And if this doesn't happen, in a larger scale, in a whole society, then it as well deserves and in the longer run, it will collapse. That is actually an evolution of a kind