Sounds to me like your competitor somehow has a series of web pages being indexed by Google, each one optimized for a different set of keywords & title.

I wonder, do the web pages use any sort of framing (of sorts)? If so, maybe the optimized pages display a "common home-page" where that "home page" is a common framing element (or gathered as a scripted "dynamic" element using PHP, etc.) to then be displayed within each of the optimized web pages.

Just guessing, but it might be something to look at. Look at the meta tags and see if the title tags really are different. Pretty tricky if that's what they're doing, and getting away with it.