I don't agree with this.
Roughly 90% of owners clean up their dog's poo. Requiring the vast majority to pay for the actions of a minority will a) not incentivise the minority to change behaviour and b) punish people that are doing the right thing (e.g. why should I keep being tidy when I'm paying to be untidy).
You'd get much the same effect putting the whole poo pickup tax onto general rates - lots of innocent people paying for the actions of the minority.
I initially thought the idea of using DNA was crazy but as long as the test can be made cheap enough I have decided I support it. Whack the people you catch with a big fine ($500?) and publicise the heck out of what you're doing, and I think the behaviour will suddenly trickle off to the point that the programme becomes cost effective.