"...in certain very specific areas." I grew up near quite rural areas and a certain level of mechanical innovation was expected. You need to use the power take-off on a tractor to run an irrigation pump temporarily until you can buy a new one? Break out the welder. The snow plow broke beyond reasonable repair? Break out the welder.

For further evidence, watch any TV show making fun of rednecks. You'll typically see things like an excavator used to create a waterfall for everyone to swim through, or someone fastening a lawn chair to a beefed-up, self-propelled push lawnmower to make a riding mower.

City life very well might increase innovation in certain fields. I'd posit that country life increases innovation just as much, but in different areas.