You have to remember that these are Trump fans.He is not back tracking.
He said even before the Oval Office spat, that he is ready to sign over mineral deals, but wants security guarantees.
He is saying the same thing now, so no change.
The idea that he regrets the fight must mean he is "backtracking" and "Donny won" in their minds because they subscribe to the whole "never say you are sorry, always express dominance" etc.
They can't see that he isn't backtracking, he just wants to move forward with the deal.