I've thought about this idea for a really long time.
I think it's a great idea, but the law would have to been opened up to those who use all alternate forms of transportation, such as walking, public transportation, car pooling, etc. You're right about the "proof" aspect. Any ideas? (obviously, having your bike parked outside the office is pretty good proof, of course).

There is also the opposite scheme. A user tax that drivers would pay. Funds would support improvements to bike trails. Yes, we already have the gas taxes people pay, but those mostly support highway improvements. The user tax would be a punishment tax, instead. For example, it could be applied when they bought their cars.