The Coronavirus Information Page, linked at the top of the hilton.com homepage (
https://www.hilton.com/en/corporate/coronavirus/) Seems to be pretty clear:
Sounds to me like you are right and the agent is wrong. I would be interested to direct that person to this page and ask them to reconcile what they said with what the page says.
The way I read it, if you have an already-booked stay - one that was booked before this update on March 25 - which is scheduled for arrival prior to June 30, you can cancel without penalty up to 24 hours in advance of scheduled arrival. In addition to that, if you MAKE a reservation now (between this 3/25 update and 6/30), for any arrival date in the future (it goes without saying that the 'future' should include *next* December, but obviously wouldn't include *last* December), you can cancel that reservation up to 24 hours in advance of the scheduled arrival.
I would call back. Or reach out to the social media rep here on FT