Well one can argue that If you buy distilled water and make it sterile (that doesn't mean pyrogenic free as you well said) with a .22um filter it should be probably very ok and not contain endotoxins at any dangerous level.Sterile and Water for Injection are two different things. Sterility is not enough. Sterility only means an absence active bacteria.
Water being injected must be "pyrogen free", and sterilized distilled water isn't.
I'm sure a lot of UGL and bullshit Amazon brands of BAC isn't pyrogen free, but isn't a great idea to use it.
If you have a hard time getting pharma BAC, buy "sterile water for injection" and add benzyl alcohol to make BAC.
But yes it's best to use non pyrogenic water aka sterile water for injection