Here are the terms and conditions from
https://www.americanexpress.com/us/c...-0#offer-terms
During each year of your Card Membership ("reward year"), you are eligible to receive up to $250 total in statement credits on your Card Account for eligible purchases made directly with participating Hilton Resorts with your Hilton Honors American Express Aspire Card during that reward year. Your first reward year begins on your account opening date. Each subsequent reward year begins on the anniversary of your account opening date.
Eligible Hilton Resort purchases must be made directly with the participating Hilton Resort and charged to your Hilton Honors American Express Aspire Card account for the benefit to apply. Incidental charges (including charges made at restaurants, spas, and other establishments within the hotel property) must be charged to your room and paid for with your Hilton Honors American Express Aspire Card at checkout in order for them to be recognized as Hilton Resort purchases. Visit
hilton.com/resorts for the list of participating Hilton Resorts. Purchases made by both the Basic and Additional Card Members on the eligible Card Account are eligible for statement credits. However, each Card Account is eligible for up to a total of $250 per renewal year in statement credits across all Cards on the Card Account. Please allow 8-12 weeks after the eligible Hilton purchase is charged to your Card Account for statement credit(s) to be posted to the Account. Please call the number on the back of your Card if statement credits have not posted after 12 weeks from the date of purchase. Card Members remain responsible for timely payment of all charges.
Nothing in those terms says the room rate is excluded. There is a room rate exclusion on the $100 property credit, but that's a separate benefit. Perhaps the phone rep got the two confused. I would hang up and call again.