I have a Facebook account which is associated with one e-mail address. A friend sent an invite to another e-mail address. Since then I keep receiving the invite again and again.
Last time I added the second e-mail address to my Facebook account settings. When I did that I got a weird e-mail telling me that the e-mail address was removed from my account but I can still use it. However, the e-mail address is still in the settings, and if I search for it I find myself on Facebook. Facebook then sent another invite to that address as if I don't have an account.
The worst part is the content of the e-mail itself. It shows the person who invited me and "Other people you may know on Facebook". The name of each person is a link. However, those links are useless. If I am logged in, they take me to my Facebook home page. If I am not logged in, they take me to a page where I can start creating a Facebook account. There's no way to get information about the people listed in the e-mail. To add the friend who sent the invite, I had to search for him by name. Looking at the links for various people, I see that they're all identical and they are the same as the "sign up for Facebook" link at the bottom. Because of that it doesn't matter which link you click; all the people listed are basically being used as advertisements for Facebook.
Besides creating a Facebook account, the only thing I can do with the invites is ask Facebook to stop sending e-mail to that address. There is no way to reject one particular invite without preventing all future invites. I suspect that this "unsubscribe" option is designed to stop people from using it.
So, yes, it kind of looks like a genuine e-mail, but the way it's deceptive and repetitive makes it spam. I don't know what to do about this. I don't expect Facebook to listen to my complaint, complaining to their ISP(s) would be silly. It's too bad that deleting my account isn't an option because of so many other people who use Facebook. (It is to social networking what Windows is to operating systems.)