C'est Moi

It should be simple. C'est moi" means, "it's me". But, more and more lately I've heard this phrase used instead of "You're welcome" and other pleasantries. I've had a hard time with "De rien" (it's nothing) even though it's in the dictionary, but, C'est Moi? Everyone, even educated people say it.

So for the next few days, I'll be running around town using "C'est moi" all the time to try to drum it into my head. By the time I get used to it, it won't be the thing to say and I'll have to learn a new "phrase of the instant".