Maybe you could have proposed your "battery test" on the dud/blown speaker in the first place, rather than make some dubious claims that an out of phase speaker makes a buzz, produces zero sound, and/or "mathematically" drops out the lows.
That might have been helpful....
"A blown speaker has a similar effect to one that is miswired, moving opposite to the working one in the lows, and good potential for buzzing too."
Interesting that a blown speaker is so similar to a miswired speaker, of course it would move in the opposite direction............it's just physics isn't it?