Do you believe House would really have spoiled that book?

Q for people who know the old TV series House:

I watched the first three seasons of House earlier in this century and then stopped. Recently picked it up again at season 4 on Prime Video. Season 6 ends when House & Cuddy finally get together romantically.

Just before that, House gives Cuddy a valuable collector’s item, a rare book on surgery written by her great-grandfather. House inscribed it on the flyleaf in ink to Cuddy and her boyfriend Lucas.

Does anyone really believe that he would have mutilated this valuable volume by writing in it—and shown the bad judgment (and poor observance of wise social custom) to inscribe something to an unmarried couple?

House may not be much for social convention, but surely he would not take such a destructive liberty with this treasure of medical history—or stick Cuddy with a permanent reminder of a temporary relationship.

I think this was a horrible lapse of House’s character, scripting an act that I think he never would have done, and I wonder if anyone else agrees with me.