I'm not sure there really is an disagreement
Before I built a treated room (and for a little while after wards) I would burn heaps of mixes on to CD and play them in the car(s), other rooms, other setups etc ad nauseum. Adjusting the mix each time.
Now I don't have to do that because I can trust the combination of my ears, monitors & room and know that what I am mixing translates faithfully elsewhere.
Its 'easier' if all the conditions are right but if not you can still do a good job if you know your own gear and any of its short comings.
Sure 'professionals' don't test their mixes on other systems because they have paid a lot of money on good gear & room treatment etc not to have to. Likewise if they don't know their own gear they can still not pull a good mix.
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