I don't know about any shops scamming the VA. I have all of the legitimate paperwork from both the shop and the VA. I used the last 4 months I had left of my GI Bill.
I think the main thing is you have to be enrolled in a full program with the understanding you are completing the courses with the goal of using the certification as a career. I am hoping to be an instructor eventually so I am completing the entire course through Divemaster. If anyone would like to see the actual paperwork, I can send it to you privately.