Thanks Slojab. That's great info.
In that link, we have
[6] Under the rule, an order can be marked “long” when the seller owns the security being sold and the security either is in the physical possession or control of the broker-dealer, or it is reasonably expected that the security will be in the physical possession or control of the broker or dealer no later than settlement.
So now, if we go back to the example in the original post, if an investor wants to sell 100 shares that he owns, MM may indeed sell first. But since the rule above applies, the transaction shall be marked by long and thus won't show up as short in FINRA data. Am I correct?