That is a very interesting theory about Filch, however far-fetched.
If he wanted to prove something, why leave the initials R.A.B? If Argus is his middle name and he does happen to have a first name beginning with "R," why not leave "F" as the last initial? Filch is what people know him by. . .
I seem to remember an older person speaking about Filch with Harry and referring to him as Filch!
I think that if he were born into the Bones family (by the way, we know it isn't Amelia Bones because her middle name is Susan [OotP, p139]) and was so embarrassed of being a squib that he changed his name, he wouldn't want to be recognized as R. Argus B. . .