This phrase was unknown to me until recently. I just assumed the speaker was confused and meant to say "by the same token", but it's used regularly and consistently.

Google shows around 62,000 hits for "on the same token" and 1,770,000 hits for "by the same token". I pulled up questions through Google Groups that were posted to alt.usage.english about the phrase, so it's not an ideolect. As far as I could tell, by perusing the first several pages, the phrase is used in exactly the same sense as the more standard "by the same token" and seems to occur primarily in Southern or Mid-Western American speech (this is a guess based on statements made in the blogs/pages by the users of the phrase about themselves and their locations).

Assuming I can trust what I read on the internet, I was surprised to learn that "token" goes back to an Old English root - tācen.