To be fair, if a CEO of a startup is sitting in her office 5 days a week, she's not doing her job properly. She should be out there finding funding or finding customers.
Asking your network for introductions, cold emailing, et cetera. If you can’t do this you shouldn’t be a start-up CEO.
Not necessarily. Particularly when it comes to early stage work, a lot of trust building must happen face to face.
In any case, "out there" means being "out" in the awareness of the people on whose radars you want to be. (Versus twittering about in a corner unnoticed.)