Hi Hagtech, when you get a chance, take a look at the schematics for the Ampex recording equipment- something tube like the 351 electronics.
What you will see is that the output has an *optional* switched center tap on the output matching transformer. The input, which is also balanced, has no center tap at all. Note that the input is conventional single-ended circuitry with a transformer to effect the balanced input. The ground is handled in a way almost identical to how it is done with a balanced phono setup. Of course, going balanced differential without the transformer offers the possibility of higher performance.
If you look at solid state gear, opamps are often used as a balanced (differential) input; the technique is common.
The point is in all these examples that balanced, even if it is not differential, does not require a center tap. However there is almost always three terminals (the example I gave above with two terminals was in an industrial situation) as you mentioned. In a phono system that third 'terminal' (ground) is shared between both channels.
In any event, the system works. When I did this for the first time in my home system as an experiment, about 1987, I was startled at how straightforward everything behaved. Over the years I've used a variety of interconnects, some shielded, some merely braided and all have operated without a trace of hum. Grabbing the braided cable and squeezing it with your hand made absolutely no difference in the noise floor; the system seemed to all accounts impervious. The technology to operate this way has existed for decades; I am at a loss to sort out why it had not been done sooner!