Fair question.
The mortgage is a security interest, not an ownership interest.
That’s why a lender can’t evict you prior to taking the property.
The ability to accept payoff or approve a short sale is the sole prerogative of the servicer, not the note-holder.
The note-holder (be it a hedge-fund or fannie mae) may have published requirements for servicer approval or may have the right to review it prior to servicer issuance of the approval but the letter of payoff and approval (aka the demand) is issued from the servicer.

If it turned out that was done in error (eg: the servicing contract had been cancelled or the payoff figure was wrong), then that is when title insurance kicks in.
Every deal done through an escrow company in California uses title insurance (with very few exceptions).
The attorneys for the title company would make a deal with whomever claimed a color of title.
Basically, the nature of the note being a surety interest and not a title interest, adds an extra layer of unlikeliness to that concern.
Its unlikely (though remotely possible) to ever be an issue for a buyer or seller.