No? Richard Branson invested in SpaceShipTwo which uses a hybrid rocket motor with liquid oxidizer and solid propellant. It is NOT air-breathing.
It's air-launched but the carrier aircraft is powered by traditional jet engines (not rockets).
Hum... That's the name we give to air breathing engines.
Using an airplane as a first stage of a rocket gives the exact same air-breathing advantages as using a rocket (or better, because the planes uses air as reaction mass too). That makes both equivalent on practice. Yes, an hypersonic engine makes for a larger stage, and an dual one that can operate with and without air makes for an even larger stage, but they are of the same broad category.