I have only maintained that when the primary-secondary coupling is considered, the frame of reference has been changed. With the coupling present both secondary legs MUST BE IN PHASE. And you're not going to prove or disprove that with any voltmeter or traditionally set-up oscilloscope for that matter. All your standard connections with a voltmeter or oscilloscope inherently ignore the coupling effect. They can't measure it. They don't see it.
But we have never considered the primary-secondary coupling. We are merely observing the waveforms on L1 and L2. If they are out of phase by 180, everything is well and good; if they are in phase, we have a problem. Nuf sed!