Thanks for catching the typo. It should have read "normally open start button".
Not all motors have E-Stops. If you're thinking "machine", then yes, there is usually an E-Stop. But in the process world, pumps, agitators, blowers, etc., do not usually have an E-Stop. In those cases, if a normally open start button shorts, the only way to stop the motor is to hold in the stop button (many start/stop stations have a way to lock the stop button in) or open the MCC breaker.
I keep going back to the original question: How to control a motor from two different locations, hard wired field buttons and an HMI station, and continue to use one location if the other fails in any manner. The original poster didn't ask if this was a good idea, just how to accomplish it. The logic in my post is one answer to that question.
To reiterate, I do not think controlling a motor in this way is a good idea, although I have no idea what the motor in question does. For all we know, it could be a small motor in an application that poses no safety hazard if it cannot be stopped at will.