[It makes clear sense that the CAA are only permitting G-reg aircraft in this trial. They (the CAA) have full control over these aircraft but have absolutely no controls over the FAA registered N-reg aircraft or the equipment carried therein or the certification of the pilots flying those aircraft.]
Actually it is not clear at all. My understanding is that the CAA wants to gain experience of GPS approaches. They are simply not going to get much by their current restrictions -- there are not enough G reg aircraft properly equipped, a legacy of all the years of Euoropean and UK legislation making it difficult to obtain an IR, unlike in the USA. The only way that the CAA is going to be able to obtain what they say they want is to open up the trials to aircraft that are properly equipped, and that simply means N-reg aircraft and other European registered aircraft.
By the way, one could also question what on earth the CAA hopes to learn about GPS approaches by this solely UK based trial that is not already known perfectly well through 1000's of GPS approaches in the USA. They only have to hop on a flight to the USA to see how it is done.