Pretty sure that is just their tactic to scare you into paying.
Have a look at this website
I'm no expert on this, but my understanding is that basically this stuff comes under private contract law. So they can only try and sue you for "reasonable" damages. If you were parked slightly over a line, and there weren't other cars about anyway, then it's not "reasonable" for you to have to pay anything.
Even if you, say, forgot to get a ticket, they could only claim what was "reasonable" from you (e.g. a few quid), and not, say, £50 or £100.
There's some useful advice on that link.