I don't think anybody could do all that at once without at least putting one of them on hold. Certainly I couldn't. I'm notorious for not being able to fathom the words if the sound is bad or the accent is strange to me. You should see me at an airport gate when they're gabbling unintelligibly into a mic. I like to think I'd have said to the guy on the phone something like "look, it's a bad line, I'll call you back in a bit." And then deal with the one who was trying to talk to me while I'd been on the phone. I suppose there's also a sign - raising a hand - to somebody who's talking to you, to tell them to wait a minute. Under the circumstances they should have been able to see why.
But in practice, I don't know if I'd have handled it so smoothly. I have a habit of getting so bolted to the detail of what I'm trying to do that I can't see the overview, which in this case would be "hmm, two inputs at the same time, better switch one of them off." I manage it sometimes but it depends on my state of mind.