That's absolutely true. And also, whether or not they will take it further also depends as well as whether they win or not if they do will.depend. The one that I had where they backed out the day before the court case was against Parking Eye. There's loads of information about this and all the other private parking firms on the Martin Lewis Money Saving Expert parking forums that I and others keep recommending. You'd be much better off looking on there and judging for yourself what the likelihood of them taking it to court or winning if they do, or not based on the reported cases.
There is so much misinformation and misunderstanding here on what actually can or might happen. Somewhere between all the false common law "they can't, you should always ignore them" stuff, which hasn't been true for awhile now, and the "they will definitely take it further/take you to court" stuff, which just isn't true, lies that actual truth. They can, they might, how likely they are to depends and whether or not they are likely to win, or not, if they do, also depends. If you look at the specialist forums you can judge likelihood for yourself. My personal position is that, judging by my own stats (2/12) and what is reported on the parking forum (few wins) you can ignore until they issue the notification that they are taking it to court, then you do the FOI request and see what their evidence is, then you decide whether to offer to pay something or proceed to court.
If you cba with all this, pay it. You probably could get away with not, if you cba with the research and paperwork.