You're actually right, I just looked it up to be sure, Marvel AND fox have the rights to Skrulls in the cinematic universe same as they can both use Scarlet Witch and Quicksilver. But the Chitauri and Skrull are separate things. I stand corrected.

They started out as the Ultimate Universe version of the skrulls, when they eventually showed up in the 616 (the main marvel comics universe) they were defined as being a separate species. It's more of a semantics thing, the same way FOX has the rights to the term "mutants" which stops Marvel Studios from using them…

The Skrulls are tied in with FF at FOX