You’re 100% correct in your interpretation of the strict grammatical meaning. I think maybe ‘not giving a shit’ existed as a turn of phrase first, and ‘giving

You’re 100% correct in your interpretation of the strict grammatical meaning. I think maybe ‘not giving a shit’ existed as a turn of phrase first, and ‘giving a shit’ is sometimes used (incorrectly in the grammatical sense, but ok in the colloquial sense) as the complete negation/opposite.