If you're looking to just change categories so that you can book a specific room, you certainly can do that. Your TA is wrong that that is considered a cancellation and rebooking.
BUT, was your original booking a last minute reservation (one of the *GT bookings - IGT, OGT, or VGT)? If so, that one can't be changed without cancelling and rebooking.
If your original reservation was a GTY booking (one that specifies a category, like 9B GTY, or 4A GTY) and you have since been assigned a room, that can be changed without cancelling and rebooking.