These features exist in Flash Pro.
An Icloud advisor named Archie just told me they exist in illustrator so go ahead and buy the whole Creative Cloud because I had Photoshop CC and you can't have two singles apps. He followed me all the way to the bank. Would Adobe Creative Clould lie about this to get you to pay $49 a month. How low can Adobe Creative Cloud go!!!!! I even asked where they are hiding them and he insisted Illustrator had it. I once thought Adobe was a good company.... Does any one know if it does exist in the new Illustrator CC.
No, Illustrator has never had bones and skeletons. Flash CC doesn't have the bone tool now either as it was removed, along with a few other features, for the CC release. You can read more about what features were removed here, http://forums.adobe.com/message/5420124#5420124
However, the way to get things to move like you're wanting is to group objects together and then use the rotate tool where joints would be on the shapes.
Yeah, inverse kinematics has been removed from Flash CC. Not sure why. So Flash isn't an option.
You could do similar things in After Effects using the puppet tool, but that would be a new, complex app to learn.
If you were misled by the phone support, I would call them back and demand a refund.