Interesting!
My sister does this on behalf of her children (3 and 7) when they come over. They'll be playing w/ a toy and it's time to go. She'll say "Ask your Aunt if you can take it home"
What a strange position to be put in!
Who takes toys from places they visit?

I guess OP's friend is what they will grow up to be.
BTW, I have said, yes, they can borrow it if it's super uncomfortable and the kid is clutching it at the front door as everyone is standing around ready to leave. Haven't gotten anything back over the years tho.
What I say most of the time is, "I'm glad you like that so much, we'll have it here so you can play with it next time you come over"
It must be some disorder or symptom of one. Someone should look this one up in the DSM manual for us!