Here is (or was) a third example of a manufacturer recommending water as a stop bath and against using acidic stop bath. It comes from a post at Photo.net. I am going to quote the whole post and then give a link to the post. Please note who posted it, someone from Ilford Imaging USA, so I assume he is giving authentic information about Ilford's former recommendation.
Please note one subtlety in the post below, which is that it's not clear whether the author is referring to film processing or print processing, though it seems he is more referring to print processing since he mentions "Dektol". However, the original post in the thread was in the context of negatives, i.e. film processing.
Also note that the author of the quote below does not say that there is anything wrong with using water these days, only that a mild acid stop bath is OK to use.
"Water or stop bath can be used after development. As others have pointed out, stop bath will be quicker, but in practice, a water bath will also stop the development rather quickly, especially since by the end of the development time, it is going rather slow anyway.
In the past, ILFORD recommended using only water. The reason was that if the development is halted to quickly, you can get acid-shock reticulation, which is the result of the rather violent chemical reaction taking place on the surface of the film. With today's films, and less aggressive stop baths (such as the ILFORD ILFOSTOP, which is citric acid based rather than acetic), the danger is eliminated. However, if you are using Dektol, you may run a risk with using a stop bath, as the developer is much more active than those usually used for film.
I would not recommend skipping this step altogether. While that may work okay with some developers, in many cases it can lead to dichroic fog on the film, especially if the fixer is not totally fresh. This fog will show up as a slightly silvery sheen on the film, or can sometimes have a color to it, resulting in an apparent stain. The use of a stop bath or at least a good water rinse will eliminate this possibility.
David Carper
ILFORD Imaging, USA"
Here's the link:
https://www.photo.net/forums/topic/34634-stop-bath-vs-tap-water/