In this case, the simple answer is no. The little man you mention will ticket you if you leave the site without moving your car. I’ve personally witnessed 3people arguing with him over his overzealous ticketing.
On the other side of the argument, he is only doing his job and why should the Car Park owners pay rates only for people to park for free and then shop at one of their competitors?
I think the same rules apply at many of the other free, private car parks in (and out) of Wrexham. Somebody will no doubt find a way to blame the Council but they have no control over the private car parks.