You're absolutely right. I know this from experience as well.
There is no chain, it just increases slightly after each 100 Pokemon you encounter. It caps at 500, HOWEVER...the method is bugged, and there is only a 3% chance that you will get the increase once you hit 500. That's why people are getting to chains of over 1,000 (I myself got to over 4,000) and still have no shinies.
It's a crap method.
Just FYI, for the counter to go up you have to actually faint the Pokemon -- and that's why this has been dubbed the "Murder Method"