No, you got kicked because X1 people are probably the most annoying to deal with online. They are either 10-12 year olds that think that since they have the fastest car they can do whatever they want. You cross their path, they'll bump you right out.
As for the "any car" part, they probably allow anything but the X1, that includes road cars, tuners, LMPs, race cars, etc. etc. But NOT X1/F1. If you want to use your X2010 badly, go for a lobby in Top Gear Test Track that says "fun, drag, trade" or anything similar. People there are a little bit more tolerant.
My problem with online is freezing and disconnection. I have a very fast connection, 5 star quality and 5 bar connection my friends say... but whenever I join a room with 4-5 star quality/bars and after 30 seconds:
"You have been disconnected from the server."
Freezing - Arguably the most annoying thing to deal with. My disc has no scratches, and when I go into a lobby, I go out, after 1-5 minutes my screen freezes, music stays the same, and I can still hear people. But I can't move. When I leave to the XMB, my PS3 bleeps 3 times and then restarts. Fix this, PD.