It's common meaning is to imply 'on the other hand' so the corruption above doesn't hold with me.

I wouldn't say that its use is common in the UK - leastways, not these days - but it used to be in fairly frequent use years ago.
However, to me it always seemed to have the connotation of, "springing from the same source."
E.g: Understaffing means that many buses are late. By the same token, most of the staff are tired and surly."

(ot something of that sort!)