I am not saying that you should not attempt to get schedules E but they are really a look in the past while a current T12 and RR is giving you a picture of the current operations. On top of that, schedules E show annual numbers only which are fine for a high-level review of past years but not granular enough for a detailed analysis of current operations.
Regarding the accuracy of T12s and RRs, reports prepared by a reputable third-party management company are generally accurate. The highest risk of fudged T12s and RRs is with self-management - I venture to say that someone who is purposely giving a prospective buyer an inaccurate T12 and RR will also cheat on tax returns so a Schedule E in these situations will likely underreport collections and overstate expenses. In any case, the more doubts you have about the accuracy of the numbers, the more you have to dig in and ask for bank statements, invoices, leases, etc. and verify that they are accurate. Even once you were able to reasonably verify the accuracy of both collections and expenses, you still have to determine how you would be able to run the property.