This is something most true cat lovers, like me, can attest to very well. My tabby Elsa often comes running when she's startled or stressed, and loved to lie in arms purring as she recenters.

If I've left her at home and have been gone longer than usual, she responds with great enthusiasm when I finally return.

I've had cats who were less attached then Elsa or who showed it differently, but I've never had a cat who truly deserve the independent, aloof reputation.