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!
Okay, we can go with this statement. Just start by accepting that the lingo AGREES with your statement. It does not invalidate, argue against, or contradict what you said.
All observed voltages with a meter or scope are based upon the reference frame you impose upon the system. Tap L1 and call it zero and you get in phase waveforms at N and L2. Tap L2 and call it zero and you get in phase waveforms at N and L1. Tap N and call it zero, as you have, and you get out-of-phase waveforms at L1 and L2. The fact that you can retap at different locations and get different waveforms is why it's called an apparent waveform. Its appearance depends on your reference frame. It doesn't make any of them less real or less accurate. [And yes, I am presuming you're using a scope that doesn't lock it's reference probe to the local ground]
N = 0V is the most commonly used frame for obvious reasons.
Rick et al, in the prior thread were purists. That means they wanted to model the transformer in the circuit. Unfortunately they didn't understand that you were never going to do that. You don't ever have to unless you want to understand why Mivey et al were butting heads with Rick et al. Mivey only modeled without the transformer, Rick only modeled with the transformer.