ok I see where you are coming from and you make a great case, but fakie does not necessarily only reference the tail slap as its means of definition. for example BMX and inline both use the term too, and to both it means to go backwards. On a board it is more complicated, but you can ride fakie WITHOUT doing an ollie, so your point is not exactly accurate. It is more about foot position on a deck, which is not really applicable to skiing, inline or bmx.
saying this again, but...
Switch and Unnatural essentially mean the same thing. If you are goofy, riding regular is switch. If you are right handed, writing with your left hand is switch. If you are right footed, most cases you have a natural inclination to turn to the left opposed to the right. Turning the opposite way of you natural inclination is more sketchy, less comfortable, OR your switch. Whether right or left is switch or natural depends on the rider... but other than which shoulder you look over, there is only one way to ride backwards. So in the end fakie makes the most sense, and it is consistant with every other action sports definition of going backwards.
Cab is a trick (fakie 360)
people have adapted it to mean fakie generally, but technically you are correct it is a fakie 360.