Does anybody honestly do anything but stick their hand out (Statue-of-Liberty style)?
On a more serious note:
I'm surprised they're even attempting this with medallion cabs. I honestly don't see the need here - Uber's availability in NYC is decent... could be improved, certainly, but there are well more than enough gypsy cabs/car services around to tap into, it seems.
The NYC medallion system is one of the few that I think works well. Unlike in other cities, the rules that Uber would potentially be violating are those which only affect medallion cabs, and explicitly exclude car services like Uber. (The intent is to have the medallion cabs resemble a 'public' transportation system more, in that they cannot refuse service to anywhere within the boroughs, cannot refuse passengers etc.), while the private cab companies can do whatever they damn well please, more or less.
I'm not sure what Uber has to gain by doing this - it's a hefty risk, especially since the forces they're probably up against here in New York are very powerful and very well-funded, and the laws are already rather lenient - they've been able to establish a successful business already without pushing the envelope.