Recombination can absolutely happen inter-genera and even inter-family.
There's some evidence that Ebola got its VP40 from bats, or vice versa. Meaning that an RNA virus somehow got its nuclear regulatory factor from a bat. We have no idea in science how that happened. But we know there is homology! I can't find the link at the moment, but when I do I'll add it here. It's not actually that important to my argument.
There are also examples of inter-family recombination in viruses that are much more down to earth.
See here: https://www.virology.ws/2016/10/27/genome-recombination-acro...
And you might be asking yourself, after reading that link "Why is it always bats?? Isn't that /suspicious/?" It's actually in keeping with everything we know about bats and their role as a viral reservoir. Lots of viruses cross paths in bats. See this other detailed post I wrote a while back: https://www.reddit.com/r/science/comments/gehvui/why_do_viru...