Are pronouns nouns that get paid?
Consider the two constructions, “They objected to me singing” and “They objected to my singing”. In the first, the objection is to me (perhaps they’d rather have someone else sing), in the second the objection is to the singing.
The pronouns him/his, them/their, and it/its function similarly, but no corresponding distinction can be made using her.
Just another oddity of this weird language we use.