That is only true if there is no content duplicated between them which your example is not great on, AND there is no phase issue introduced via another method, such as EQ which many styles of EQ actually use phase to introduce a magnitude shift.
So for the first example, a common problem on live recordings, when you might for instance have bleed from drums into Vocal mics, or guitars into vocal mics, etc. The content is not identical, but can still introduce phase issues, even in close micing scenarios. This is why on larger gigs you might for instance delay all inputs to the proscenium line appropriately, or delay to the system, but to fix issues of phase from the system, and phase issues between mics as well, at least as good as can be expected in such a compromise.
This applies in live recordings or in live room recordings where the band may be all together. I think we agree on this in principle but it did need to be clarified a bit.
For the second example, many EQs introduce phase problems as a fundamental function of how they work. You hear these phase problems audibly as a magnitude change, though typically more complex as the are really comb filters across frequency bands dependant on the filters in question. For instance on some EQs merely sweeping frequency bands in particular ways, even if there is no magnitude change in gain, can cause a phase issue to become apparent, even if the EQ sounds decent otherwise. This is also why I stay away from the Calf EQs on linux, as they have audible phase issues introduced as you utilize the EQ.
So as a counter example, when introducing a phase problems you have far more complex signals, and you have introduced a slight timing shift in a particular frequency. The problem is that you have a balance between resonance and overlap of frequency bands. The gentler the slop of the frequency filter, the more overlap with the original signal or nearby bands depending on the design of the EQ. So you have two signals happening, one 100% in phase with the original as it is the original, one something other than 100% in phase, which will cause interference at frequencies dependent on the phase issue and frequency in question, along with the strength of original vs modified phase.
For anyone reading this, I strongly suggest you do tests, and see exactly what I am referring to. Seriously grab the Calf EQs and compare them with other EQs. Look at the measured phase response in a dual-fft, especially in the slope of the filters, and see how much the change is audible. This is part of why some people prefer certain EQs to others. This technically could apply in any frequency specific processor (So full bandwidth processors like a standard compressor or gate generally don’t worry about this).
Or for more reading on the topic(More so you know it isn’t just me that says this), a quick google shows up articles like the following quickly (See #7): https://www.izotope.com/en/learn/12-common-eq-mistakes-mixing-engineers-make.html