I think this is generally true for a particular sentence. But I've read scripts by emerging writers in which practically every action verb was a strong verb, and the result distracted me from the story. The strong verbs were not the result of a particular writer's authentic voice but a tell that a writer was following someone else's advice, thesaurus in hand.

BTW, an adverb can also modify an adjective (as in "generally true" above), so the strongest verb principle wouldn't apply there. It seems possible that too many modifications of adjectives might make the action paragraphs seem waffley and less direct.