I am confused by what right the celebrity is claiming a copyright in the photograph.
A proper DMCA notification can only be sent by the copyright owner. The copyright in a photograph, in the first instance, belongs to the photographer. The photographer may be under contract to assign, or may later assign, the copyright to someone else. But I do not own a copyright in a photograph which someone has taken of me.
The celebrity may have a right of publicity, but that is not the same thing as a copyright, and cannot be the basis of a DMCA notification.
There is some general mythology about the purpose and effect of DMCA notifications. This procedure was provided in order to allow an "out" for webhosting companies, and to relieve them of copyright infringement liability if they follow the procedure - it's not about you at all.
The webhost can avoid liability if:
- They receive a DMCA notification (with the elements required by the DMCA);
- They notify you of the notification;
- They provide a time period for you to respond with your reasons why the notification is wrong or otherwise invalid
- If you do not respond, then the webhosting company takes it down
- If you do respond, the webhosting company does not have to judge who is right and who is wrong, and may leave the material up without incurring liability.
The basic idea is to provide a mechanism for copyright owners to have material taken down unless the poster of the material speaks up and claims a right to post the material. A lot of folks - webhosts included - do not fully understand that the material can stay up based on almost any response by the webhosting customer. Most of the time, the customer does not respond, and the material comes down.
In a situation such as this one, again, I would question the celebrity's claim to own a copyright in the photograph. However, that issue is only limited to responding to the DMCA notice, and not to other issues (such as the right of publicity/privacy) that they celebrity might raise apart from the copyright claim.
Happy now?
But personally, two people enjoying each other in whatever consensual way they see fit is their own business, and the photographers and the audience here have what I consider to be a serious personality disorder which requires professional help well beyond my area of expertise.