Smarkle,
I wish I would have had the same experience that you had with Apple stating the lightening connector was faulty. I also tried to state this to the rep over the Internet and in person to the genius bar and they refused to listen stating that the iPad was "abused". I purchased a replacement iPad at a discounted price.
Others on the posts: It could very well be faulty - my daughter also reported that she went to unplug the connector and that it had snapped off. There is no way she could have physically broken it off seeing as though she's only 11 years old. If the connector was made properly it should be impossible to snap off, as one other person on this post stated.
Don't bother attempting to take the iPad apart. It does not do any good. The connector is encased in a conduit so it is impossible to force the broken peice out from the backside of the conduit. It is completely enclosed by a metal casing. The only way to get the broken peice out is with very small pliers. If you get lucky enough, and obviously have the right tools you can grab it with the tool and slowly pull it out. I do not recommend the super glue trick. It just forces the peice further in when you attempt to take the remaing wired peice and press it into the broken off peice. Not a good thing. I tried everything and anything I could on find based on suggestions over the Internet. I even took the iPad to my jeweler who did not even have a small enough tool to reach up there and pull the broken off peice.
Again, I chalk it up to a faulty connector, but ufortunately Apple won't own up to that. My connector was the original connector that came in the box when the iPad was gifted Christmas 2012.