That was probably a very specific issue SOS were talking about and not a normal way of working. Also don’t take SOS as the be all and end all of correct information.
I would suggest you’d be better off learning to sing in the traditional way,99.99999999% of singers have worked since headphones were first used (Incidentally, when the singers of the 40’s and 50’s first started using headphones in the studio, a lot of them had tuning problems to start with as it was a completely new experience to them, they soon got used to it though)
Either get used to singing with phones on or have the one ear on ,one ear off method some singers like. You’ll get better at it the more you do, and I’m sure it wont be long before it feels completely natural.
If you get used to doing it the way you are, then you’re setting yourself up for problems in the future when you work live with in ear monitors or work in other studios.
Like with anything new, it’s always best to start with good practice rather than bad, you’ll only have to undo the bad practice later on , and it will be a lot harder.
MC