I remember reading it when I was researching the requirement for "Special Priority" (which I now have) exemption.
In England and Wales, there are 11 large regional water and sewerage companies, plus a number of smaller "water-only" companies.
Scotland and Northern Ireland have different structures, with services largely in public ownership, so they do not have the same privatized model as England and Wales. So the two English companies that you checked don't prove that all companies exempt Blue Badge holders.
I have no problems with people assuming they are exempt and not checking. If they get fined I will not be the one paying.
Applying Pascal's wager proved that it is logical to check with your local provider.
Howevr, if you do research all the companies and find that they all exempt BB holders I will abjectly apologise.