That's of course wrong. You can always drop resolution or details on a GPU, but you can't generally reduce the CPU requirements of a game. I'm still happy with my HD5770, but my i5-3550@3.9/4.1 is too slow for my needs - and yes, I mainly play strategy games.
Exactly, and that's the point I try to bring up when people carelessly dismiss the CPU. Fact is you can get any game to run reasonably well on a GPU as old as an 8800GT at 1080p by simply reducing settings. The same cannot be said about CPU's. If you're having performance issues due to not enough CPU power, you're essentially screwed. You can do things like reduce audio quality, but that generally doesn't' do much AND there are fewer and fewer games with that option.
The other issue is that you can pretty much always put a more powerful GPU in, and even if it's an overpowered GPU you can transfer it to a new system easily enough. If however you skimped on the CPU, particularly if you're in a situation where say you opted for a Core 2 Duo instead of a Core 2 Quad back in the day, you're not stuck in a situation where you ether need to buy and overpriced and quite likely used Core 2 Quad, or spring for a whole new system when you weren't quite ready to.
Bottom line is, don't skimp on the CPU! That includes you guys who think you're getting such an awesome deal by saving $80 going with an AMD FX instead of an Intel i5