There are a few moments in that NJ perf where you can hear the audible 2 layers when there's a suitable time to sing some lines so technically it's "live". This is pretty much the standard way to do it for all groups. This is kind of the point I wanted to make, to most K-Pop fans these 2 performances are just 'live because I could clearly hear them sing' and that's the end of the analysis. Then these 2 get compared and one group gets dragged for bad vocals.
I want to point out that IVE does the exact same type of performances quite often where only some parts are sung, not trying to single out any group.
Hearing breathing or other noises isn't always reliable because even your very own phone or computer comes with built in noise gate, it's a pretty basic feature so the headsets or postprocessing of the audio also has it. If set high, it will register absolutely nothing until you properly sing and cross the threshold. This can create LAR performances where you hear nothing but the prerecorded live vocals until someone actually decides to sing.
There are also many cases where breathing noises have been part of the backtrack since they've recorded it while dancing so that's not really reliable either. They can make it sound just the right amount of 'uneven' in postprocessing or chop up a version out of multiple recordings, whatever it takes to make the illusion credible.