I started lifting weighing about 150lbs. If the size on my arms was averaged against the overall weight gain, it would be about 15lbs for every inch.
No one is saying that it is impossible to gain some size without that much overall weight gain, however, if you plan on making much progress beyond the minimum, it will take overall body development.
There is a reason why there are no people with arms close to 20" who are under 190lbs of body weight. If extreme growth of individual body parts worked outside of overall body development, at least some individuals would experience that extreme.
I think calves are possibly the only muscle group that I have seen just look disproportionately huge on people who don't even seem to lift. That one muscle group seems to stand alone and be almost completely dependent on genetics aside from relatively less growth from strength training.