From Facebook Developer Wiki

yes... you can rsvp to events, but you cannot properly invite people to them through the api!

Additional rule: - You can't use events_rsvp for closed events. Even if application is the creator of this closed event.

[edit] THE RIGHT WAY THIS SHOULD WORK:

With a session and/or extended permission, an app can RSVP for people. How many events are most apps going to be the creators of? A lot of possibilities open up if you can show other events in your app, and allow people to RSVP for them in your central event hub. This would also work nicely in conjunction with how I'm suggesting Events.getMembers should work here: http://wiki.developers.facebook.com/index.php/Talk:Events.getMembers

James from FaceySpacey.com (email me at james@faceyspacey.com to discuss it)