Correct. Please note that Crown in fact has not two modes, but two clauses, the first checking that/if you are in your Action phase and the second that/if you are in your Buy phase. Always both clauses are checked (in order), and it is only the 'limited' set of existing cards that makes it true that always exactly one will apply.
If the order of the clauses was reversered (first checking for Buy phase, then for Action phase), you could have both effects happen, for example by Crowing a Horn of Plenty and gaining a Villa with it. Once you are done with triggered effects, you are in your Action phase, so that reversed version of Crown would now allow you to double play an Action card.
Basically it was this card (the first Action/Treasure) that established the fact that cards are just played (according to the rules), they are not 'played as an Action' or 'played as a Treasure'.