My sources don't address the specific phrase "by the same token," but the etymology of token suggests the origination of the phrase:
teach ... 1. "To teach or show, guide (obs senses), hence to guide educationally, to show to (someone) by way of instruction, derives, via ME techen, from OE teacan, akin to OE tacen, tacn, a token, whence, indeed, MRE taken, later token -- as still in E. With OE .. OFris .. and OHG ... MHG .... G ..., to provide with means of recognition or knowing.
and
TOKEN, a mark, sign, memorial, coin. ... allied to Teach. The base *taik answers to Idg. *doig, 2nd grade of *deig, which seems to be a variant of Idg. DEIK, to show, indicate;
This seems to be a case in which the phrase sprung from a direct use of the original meaning of the pertinent term, token, as a means of recognition or knowing, rather than from a metaphor based on the derivative use of token as a substitute currency or other symbol.
