No, those reps are wrong. The most straightforward way to apply a TSU to a points booking is to "convert" your room type to the standard suite while keeping the same rate plan/type (in your case a points redemption, hence the need for there to be a standard suite available for points redemption), and then eventually manually correct the rate back to the rate for a standard room or whatever room type you originally booked. However, there is a more manual process for applying a TSU that doesn't require there to be redemption availability for the standard suite.

Call in during the US business day to get the most knowledgeable reps who can handle this request. You shouldn't need to tell a good agent how to do it (the above was just FYI only as a likely explanation for why chat agents couldn't help); just say you'd like to apply a TSU and let them handle it. If they say that they can't do it, HUCA.