You place a limit order to buy FOO at $32
  Someone else offers FOO at $31.90

That scenario would result in a locked market, which can't possibly happen under RegNMS. The exchange that saw the offer for $31.90 is required to route-out to the exchange with a bid of $32.

  A HFT algorithm buys FOO at $31.90

That also can't happen. Even without RegNMS, the exchange's matching engine would have paired the value investor with the offer of $31.90, though the execution price would actually be $32. The HFT participant won't even see the ask price in this scenario.