Are you saying the divergence couldn't have been that great if there was some level of interbreeding, or are you saying something else? "Derive" seems like a strong word in this case, considering the low single-digit percentage of denisovan DNA in any modern humans.
> single-digit percentage of denisovan DNA in any modern humans
is likely a wrong description. We share around 90% of DNA with pigs, cucumber and what not (figures estimated, I'm not into Bio).