SkeletonAnimation and SkeletonAnimator don't belong together.
You need to use only one of them.
Use SkeletonAnimation if you want the standard/manual coding solution.
SkeletonAnimator if you want to use Unity animation state machines/Mecanim.
SkeletonAnimator is kind of a recommendation only if you're familiar with Mecanim's quirks and aren't doing anything complicated or you're just prototyping.
When in doubt about complexity, SkeletonAnimation may be the way to go.
This is a funny catch. But good. 😃
Not sure yet if using only one of them fixes your problem though. Please do post results.