Often the bank requires private mortgage insurance on anything above 80, to protect themselves against overly aggressive "flippers" (who buy without equity to speak of, and default and give the collateral to the bank if the price doesn't go up, and sell to repay the loan if it does - exploiting the implicit "option" a loan with collateral contains).
On REITs, the rule is they have to pay out 95% of their net income as dividends. But not "their rents". Rents can cover expenses, debt service, and depreciation - as well as contribute to net income. In practice this basically means the ongoing acquisition budget of a REIT is set by its depreciation.
When they want to buy faster than that (which is often), they issue additional securities, whether stock or debt, or borrow further from banks, typically on revolving lines of credit. When they aren't buying actively the depreciation flow pays down the credit lines.
REITs have had quite a run. They were a great play in the late 90s at the end of the bubble, the perfect place to cash out to. They have run up so much recently that just buying them at random these days, you would wind up overpaying. There are better prices in the private market. The best run REITs can still make sense, when the price isn't outrageous. But you have to value them case by case - you can't count on the market keeping their stock price rational, these days.
What's your occupation?
You seem quite knowledgable about REITs.
I bought a Wal Mart outparcel from one (Atlanta based) last year. They were later indicted for funny stuff.