If they've already authorized a transaction spending some UTXO output, then that output can't be spent again. It is already spent. The next transaction will be mathematically invalid.
Your definition of 'already' is subjective. Try imagining this from a completely objective perspective.
Yes of course if your (not mine) criteria automatically conflates that the proof of spending
order is what is being considered, because all that exists is propagation at that point.
But my phrase was to be taken orthogonally of any specific criteria as a first predicate. Meaning that it is indeed mathematically provable that the UXTO has been spent (just evidence the transaction and signature from the payer), but then in the next paragraph I stated the order is not mathematically provable in Dash's design if the masternodes lie (and nothing that Evan wrote in the prior post fixes that ... will he now try to copy my design and claim it as his own?).
Please allow that I was distinguishing the orthogonality between provability of the different attributes because it impacts how one goes about designing a correct design.