While all in their FAQ may be correct, you would have to wonder why they don't just come out and say that they are training for a FAA-PPL, and stop trying to confuse their customers with "JAA compliant PPL".
Two thought come to mind.
1. If you have an FAA PPL, you can not necessarily rent a European registered aircraft an fly it out of that country, as you could with a JAA PPL. For example, if you had access to an Irish registered aircraft, you could not fly it outside Ireland on your FAA PPL, without getting specific permissions. Some other JAA countries may allow you take their aircraft abroad on an FAA PPL, such as the UK does. This probably isn't such a big deal, as if you're based in the UK, you'll probably always be flying UK registered aircraft. Should you happen to be in Ireland, or France, or any other JAA country, and want to rent an aircraft there, you're unlikely to want to fly it out of that country. And you should be fine flying it with that country.
2. The second thing that comes to mind is the IMC rating. For a PPL flying in the UK, an IMC is a very valuable thing to be able to get. I really wish the IAA would introduce something similar here!
As far as I know you can't get an IMC rating with an FAA PPL. You can of course do an FAA instrument rating, and if you fly an American registered aircraft in the UK, you will have instrument privileges. If you have a FAA Instrument Rating, I understand you can get an IMC for some paperwork, but I'm assuming you would need to have a UK issued PPL to attach it to. Someone else can better advise you on that.
Just some food for though. The site seems to give you all the pro, I just wanted to highlight the cons that I see
dp