Should a user logged in through Facebook be able to delete their account?

In my app I give the option the users of logging in with their Facebook account for convenience. Every modern app gives its users the option of deleting/disabling their account. The question is whether I should provide such an option to the users who logged in with Facebook.

Someone might ask why not, and say that it is the natural thing to do. I am asking, though, because I have not encountered on the web such an option in sites that use Facebook login. Probably I am mistaken.

Nonetheless, to be sure I wanted to ask this question anyway.