As so often the aircraft is operated by an airline few of its passengers will have heard of, in this case "Shuttle America".
It had a Delta Airlines DL flight number. You check in at the Delta desk and it is shown in the Delta departures. The aircraft is painted in Delta livery. The FAs wear DL uniforms. There's the Delta magazine in the seatbacks. The pax will be on DL tickets.
Yet when an accident happens it is immediately announced as a carrier nobody has heard of. To the pax it would seem a technicality that it was some different operator, as far as they are concerned it's a Delta flight.
And your point is? It carries FAA authorisation and submits itself to the relevant safety audits. Sounds like pseudo-unionist BS to me.