I think you're over-analysing it to be honest. There's no play-book for every aviation eventuality. If you've done a wheels up and no fire truck races out to you, you've got little choice on what you can do. It's not like you're going to stand there waving your arms and hope people will see you before seeing your disabled aircraft.
Flat tyres on the runway are not at all uncommon, I've had a couple myself.