Dies to Removal

701.28. Monstrosity

701.28a “Monstrosity N” means “If this permanent isn’t monstrous, put N +1/+1 counters on it and
it becomes monstrous.” Monstrous is a condition of that permanent that can be referred to by
other abilities.

Monstrous isn't a static ability, it's just a description of a characteristic of that monster. You are correct on calling bs. Monstrosity is under Keyword Abilities in the comprehensive rules. It's also an activated ability. Merely putting a +1/+1 counter on it doesn't give it monstrous.