I think rating of a problem is not the same as difficulty of a problem. Rating of a problem is defined as follows "if you have the same rating as the rating of some problem then you have 1/2 chance on solving it in a contest". there are much more problems in div3 and edu rounds so it's more likely you won't solve the problem in the contest not because it's hard but because you don't have time.

I forgot where, but I've seen posts indicating that difficulty rating is different for contests in different divisions, so this is probably an artifact of difficulty calculation.

I don't remember the details, but one effect would be from problem ordering. For example, a problem of a certain difficulty might be either A in div1 or F in div3, so even if it's the same problem, more people of any given rating would solve it in div1 because people typically go in order.