I'm sorry but I tend to agree with Jurassic here (and that may come back to haunt me)

I tend to judge my reactions to an inadvertent horn by the reactions of the players. If they stop playing (especially if it is 9 out of 10) I will blow it dead, find out what happened and play from the point of interruption.

WeekendRef said: "I do not blow the whistle this entire time as I think it is the buzzer on the next court."

Obviously 2 games are going on at the same time. In this situation you have to be aware of what is going on around you. If the players feel a whistle/horn was meant for their game they will stop playing.

Now as for arguing the other side - making the call quickly (before the shot) helps sell it, if you let play continue it's hard to call something that you didn't blow your whistle for in the first place.