Could you give us some examples of the exact usages? My "cursory" search on such a common pair of words turned up 365 million hits including lots of "one on one", "down on one knee", etc. etc.

"One" here is probably being used as a pronoun thus could stand for anything, e.g. Does Suzy ride a motorcycle? Yes, I've seen her on one. Does Johnny ever trip on LSD? Yes, I've seen him on one.