I think that it is great that there are people with special interests that compliment what we do as physios. I am not sure the exact range of skills/training for sports rehabiliators but I am certainly going to find out more.
Just some thoughts that might make my viewpoint a little clearer.
When I did my degree we had a 4 year athletic therapist course at the same uni with lots of musk assessment, on-field experience etc and they were very good at it. In my 4th year sports specialisation course we had to take exams re diagnosis etc and the physios on the course scored in the 80's and 90's while the athletic therapists were scoring in the 50's and 60's. Similar training but perhaps a different emphasis on particular areas of the courses. We dissected bodies while the athletic therapists worked out of textbooks. We treated a range of both ill and injured patients while the athletic therapists worked with relatively young, healthy athletes. Certainly there was something different in the approaches because of the populations we were working with. Sometimes the specialisations may give excellent skills in a focused area but not necessarily the total broad picture. Sometimes the broader picture may lead you not to see something that a more specialised person might view. Not to say there is anything wrong with either perspective.
I worked as a primary care practitioner having to examine and decide if there was soomething seriously wrong with patients (and there were not always red flags evident but DDx skills can help when red flags aren't that obvious) or not and then treat or refer onwards to doctors as need be.
It might be just a desire to be able to make use of the legal title and billing system but both the instructor of the athletic therapists (with an Msc in Athletic Therapy) and a number of the graduates of that school decided after being in practice to go back and train through the full physio course.
I think that the experience was good for both the physio students (seeing what someone else brought to the course) and the athletic therapy students (who had a chance to see what the physio course really entailed) who were training further.
Lets hope that we in the UK have the ability to appreciate each others talents.
Cheers