Subways are public accomodations in the same sense as a sidewalk is a public accomodation. An airplane is a public accomodation in the same sense as a resturant is a public accomodation.
Go back and have a look at the .pdf I linked to as (from my brief scan of the TOC) it appears to discuss case law with respect to transportation-related issues.
I'll check it out.
And my real feelings about how it would be In * An * Ideal * World were described in one of L. Neil Smith's novels:
The protagonists were preparing to board a flying device of some sort and the only screening to which they were subjected was to be asked if they'd remembered to load their weapons with frangible ammunition before boarding the aircraft.
Here in D.C., the Metro actually closes down to the public for a few hours each night, so it's not totally apt. In New York the subways are 24 hours so it's probably more analagous there.
Even public roads are pretty much fair game now, as many courts have established the legality of random DWI checkpoint stops. Sadly, it's proabably just a matter of time until it gets extended the rest of the way to the public sidewalks as well.