Let me say, speaking as a long time buff of the FDNY, not as a firefighter. The FDNY has always done their own tests of equipment and tactics. They just don't follow the crowd. As far as I am concerned, it was the FDNY that FIRST Organized a company to stand by at incidents to assist firefighters calling Maydays. After the FDNY started doing this, then other depts seemed to come out with their own terms such as R.I.T. The big difference is that the FDNY didn't go out trying to sell their product, while other chiefs and depts pushed it in their books and promotions to help line their pockets.
The same with size up terminology. Instead of using Exposure 1, 2, etc, books started to appear calling it Side 1, 2, Side A, B, etc. I'm talking I know of the FDNY using their exposure terms, long, long, before these other terms were even thought of. (At least back into the late 60s).
Same with smooth bore verses fog nozzles. While many depts pushed the use of fog nozzles, the FDNY stood by their smooth bore nozzles for better fire attack. Many books and classes, many of which I attended, pushed the use of fog nozzles in fire attack. The FDNY never really accepted that theory, and no doubt they tested it before, rejecting it.
Over the years, many depts/chiefs tried to make their own claim to fame, when actually all they did was check out the FDNY and put their own terminology on these ideas, and a few extra dollars in their own pockets.
So whether the FDNY calls it a FAST Co, or somebody else says it should be called a R.I.T. Co., it seems to me that this whole idea started to appear only after the FDNY put this procedure into practice. (In fact, it was called a FAT Engine that only went on 2nd alarms or more).