If you book an award stay in someone else's name on the phone with Hilton, the hotel will see the status on the account the points came from and grant benefits accordingly.
If the person staying is diamond, but a non-diamond Honors number is on the reservation, they can ask the front desk to change it to their own Honors number. If the hotel agrees to change the number, diamond benefits will then be granted, but hotels may also refuse to do it.
The status of the person whose points are used is irrelevant if the member is not staying. Benefits are based on status of person actually staying. Yes, I know there are many reports of people booking an award and the stayers gets the benefits. But those people are gaming the system by being on the reservation, putting the stayer as a second person, but not going and hoping the property doesn't notice they aren't there. But as you say they stayer is Diamond they should get the Diamond benefits, they just need to show their card when they check in.