It's an interesting subject. Would its have been impossible to shoot with just the ambient light?
It's not just the reflection of the umbrella — overall, the umbrella is creating a cold, hard light that doesn't quite fit the scene (e.g. the hard shadows of the guitars by the other guy).
It's clearly a difficult scene to light (lots of reflective surfaces - e.g. the mirrorball - to reveal what you're doing). I would have lit it differently (using several gelled lights (maybe 1/4 CTO), bounced into white sheets fixed to the door and window frames). This would create a more natural looking light, but it wouldn't preclude the need for some photoshopping, so I would also shoot a reference frame with just the ambient light — so that I could paint in the mirrorball, picture-frame etc. to hide the lighting set-up.