THEMOON, you're correct, and the SPG Plat concierge who booked my room was incorrect. I only realized this when I checked my account today and saw that SPG had pulled an extra 2,000 points (for 2 nights) over what I was told the award would cost. (My points for this stay were pulled after I completed the stay, otherwise I would have noticed at the time I made the reservation.) However, because I had relied on the concierge's representation and as a result cancelled my award stay at the Westin Bangkok for the same nights, SPG agreed to refund my 2,000 points.
So, to set the record straight, a confirmed upgrade to a Towers room is an extra 1,500 points per night. Bummer.