I think binary trees are useful to know as an advanced topic, as they power some useful data structures. But I'd not consider it something every programmer should know, just some fields and some levels.
But useful though they are, I've never had to implement one myself for work (I did as hobby only). And I didn't know what inverting means.
Although if inverting is just "mirroring" the whole tree... I hate to be cruel but that's something a programmer with a few years of experience should be able to do. Is that really too much to ask? It may be useless but it's not hard.
I've found several definitions of "inverting" though - maybe the point of the question was to check if the programmer asks for clarification rather than giving up or just assuming things?
Whiteboards are a stupid medium though.