Denny Cann and Drew Beechum did a pretty thorough write up about it in "Experimental Homebrewing". It included a nod to Tasty McDole being the inspiration and had a formula and everything.
Weird though, no mention of adding more minerals to "balance" the dilution water, or using a commercial deaerator. Is that a de-oxygenator, as in boiling or carbing it first?
They mention you can just add the water and force carb it, then drink away 'til it's gone without any problems, just won't have as much shelf life.
I'm not horrendously worried about the water chemistry. For utmost consistency it'd be helpful but wouldn't hurt not to.
IIRC Tasty had some procedure using kegs and CO2 that while likely not as efficenct as the column vaccuum sprayer systems used by pros, was meant to accomplish the same thing. Edit: Looked a what you referenced- boil first, then force carb w/ CO2. Like I said, probably, not as efficient as what the pros do, but still reduces the level of dissolved oxygen.
And "won't have as much shelf life" is because you're.........introducing oxygen. Allowable level for shelf stability is no more than 50 ppb DO, with pros setting a much lower level than that (<10-30 ppb). Don't have the reference in front of me but I don't think boiling gets much below 100 ppb (edit: now that I've got the Water book in front of my- I was incredibly generous- simply boiling at atmospheric pressure only reduces to 4 parts per MILLION), and as it stays exposed cooling afterwards it reabsorbs oxygen all the while. Straight out of the tap it's going to be even higher than that. You do the math.