Hanna
Well, of course it’s up to you to decide if the clip is funny or not.
I just thought it had a straightforward answer to your question, had it not?

“Here in America when it comes to the English we mistake accent with intellect.
We think they are all smart because no matter what they’re talking about they sound quite intelligent.”

You said it yourself that according to Americans Daphne sounds posh, didn’t you?
The boy was meant to be smart, so they made him speak with a phony British accent.
And again, isn’t it funny already, even without him saying anything funny, for an American boy, whose parents are as American as apple pie, who having just barely been hatched is not supposed to talk at all, to talk with a British accent? I for one think it is.
You seem to be too serious talking of an unserious subject.