Current mirror with different emitter resistors
That quote is approximating the transistors as having fixed B-E drop.  Yes, there will be some B-E voltage variation with current, and between parts for that matter.  With discrete parts, you generally make R1 and R2 big enough so that these variations don't matter.  Current mirrors on a chip are made with well-matched transistors and usually no emitter resistors, and have a different set of tradeoffs.

Basically, the current thru each side is inversely proportional to each's emitter resistance.  Note that this also ignores the base current of both transistors appearing only on the input side of the current mirror.  If you really care about the last 2%, then you probably need a different topology in the first place.