OF COURSE BART would have a veto, or at least significant say, over local ACE traffic that directly competes with it. BART is there first, and directly competing traffic is discouraged if not prohibited by most funding agencies (like FTA). Same thing happens in SF: that's Muni territory, and GGT/AC/Samtrans cannot carry passengers between most points in SF (minor exceptions like the Toll Plaza on GGB property). GGT et al can drop off passengers inbound to SF, and pick them up outbound, but can't be used between points in SF; once you get on, you can't get off until the Toll Plaza or Marin Co. True, BART carries passengers between points in SF (and in AC territory), and AC competes with BART for transbay traffic, but that's historical accident - due to Key System ancestry, AC was there first, and BART provides a very different kind of service. In the old days of PUC-regulated private transit, those were considered exclusive franchises, and even as public agencies they still work that way.

Yes, transit funders (FTA) can pick winners, and it's usually the rail transit line (BART, light rail, etc.) if one exists. Local example for me: Folsom express buses to downtown Sacramento ended the day that light rail opened, despite providing a better (and higher-fare) service, because only one of those "main" lines could get transit subsidies and the train was it. Plus, of course, the city was paying for light rail operation into town and didn't want to compete with itself.