Completely false. The strategy game and the collection/trading 'game' are completely different activities, and it is extremely common to enjoy one but have no interest in the other.
I played MTG very competitively in my youth, and I sidestepped the scarcity issues entirely by either playing sealed/draft[0] in official tournaments, or by playing in unofficial online tournaments where cards were unlimited (I enjoyed the so-called Eternal formats where many cards had been long out of print and cost hundreds of euros at the time).
Pro players also tended to favour drafting - it had a reputation as the most strategic and interesting way to play - and while of course they also played in official tournaments with custom-built decks, quite a few of them were known for having no interest in collecting cards and simply borrowing whole decks from their friends who did have the hobby of trading and collecting (whether or not those friends played the game).
[0] A game mode where everybody starts with a small set of random cards, instead of bringing their collection.