Clem,
IIRC, the track gauge came first, then pioneer model railroaders had to figure out what scale to use. In the 1930s and '40s, many modelers used 17/64" = 1' scale. This works out to 1:45.176.
However, working in this scale must be a pain, so 1:48 or 1/4" scale was a compromise that was much easier to deal with.
Incidentally, in P:48, the minimum track gauge is 1.177" and the maximum is 1.203". See NMRA Standard S.3.1.
ChipR