Really only if you are paranoid. It's incredibly unlikely that the labs are lying about not training on your data for the API plans that offer it. Breaking trust with outright lies would be catastrophic to any lab right now. Enterprise demands privacy, and the labs will be happy to accommodate (for the extra cost, of course).
No, it's incredibly unlikely that they aren't training on user data. It's billions of dollars worth of high quality tokens and preference that the frontier labs have access to, you think they would give that up for their reputation in the eyes of the enterprise market? LMAO. Every single frontier model is trained on torrented books, music, and movies.