Let me tell you a few things about water. Water is a very simple molecule, H2O. Calling any water "synthetic" is silly, and of course, deceptive.
I'm not a chemist or engineer, but in my 26+ years of plumbing, I've learned a lot about water. I also worked for a water purification company (commercial/industrial), and learned quite a bit about the uses and purification of water.
Chemically pure water almost doesn't exist. Water is very aggressive and will absorb impurities from the air or whatever else it touches. Distilled water is very clean, but again, as soon as you open the bottle, it begins absorbing impurities from the atmosphere. My tap water at home is about 550 ppm total dissolved solids. If I run it through a consumer-grade reverse osmosis system, I can get it down to about 75 ppm. That's pretty clean. But reverse osmosis won't protect you from some diseases or organic compounds. I've worked on setups that used reverse osmosis, then de-ionization, then various UV setups such as TOC (total organic compounds) reducers. These make pretty pure water, but not absolutely pure. And of course, they also had banks of pre-filters.
Just incidentally, if you look at how a hydrogen fuel cell works, you could say that it "synthesizes" water, since the "exhaust" is water. So there's your synthetic water, I guess.
It's true that a "pure" water is good for mixing with antifreeze/coolant, and distilled water is pure enough.
Synthetic water? I don't think so.
P.S. the subject of water purification is pretty complex, but most of us don't need to worry about it much.