What happens is that some dealers to get a good discount with Peugeot or any other brand, have to be the first owners for some time, let's say 6 months. Other dealers, get their discount using high volume of sales, reducing the profit, but getting a better price from the manufacturer.
That's why it can happen, and in that situation the person would be a second owner. I would refuse if the car was sold as unregistered.
All the experience I've had buying from dealers using carwow, it never happened, but I had seen in Honest John some problems.
In fact, when using such services, it gives me an upper hand to get a better deal locally, as Cambridge holds some higher prices as standard, don't ask me why.
To use such services, I would always make sure that I will be the first owner of the car, and get the documents within reasonable time. Price wise, it's consistent. In my quote, the values were 20.700, 21.200 and 22.000. As I mentioned before, Cambridge Peugeot, no discount.
Some dealers would accept part exchange, others not. My advice is even if you have the money for a cash buy, use PCP, get the discount, wait for the document to arrive, as the finance company would be of help if there's a problem. Once all sorted, pay off the finance. Usually PCP offers a lower price too.
When I trade my RCZ for a new Sportage, buying using carwow, the dealer from kia was Coventry. Even the part exchange value was better than what I was offered around.
Your advice is valid, always be careful, but as in my quote, the offers are similar, I'm guessing that Peugeot is giving the dealers some margin to sell more GTIs.