I think this is much simpler than what you're suggesting. Careful microphone level management can handle this. No need for audio sync. I know they use the word "sync" but that's a very broad term.
If the distance from the microphone to an "unwanted source" is three times the distance asthat from the microphone to the source phasing likely wont be an issue.
There's always caveats with engineering but it's a decent rule of thumb assuming equal volume sources... I can imagine it's not too hard to detect that anyway, weve been able to do realtime fft for a very long time.
If they're actually able to "sync" (again a poorly defined term) given the problems associated with network latency and different hardware it would border on magic.