Accepted - cold tap water in a continuous flow/forced wash situation would be fine (assuming no thermal shock to emulsion; non-domestic tap water can get VERY cold in winter).
I'm unsure whether I'd agree that water temps were unimportant in a 'by changes' process though. I always make up a nice big jug of 21c water at the start, which does the pre-soak, mixes the dev and provides the plain water stop and the washes for me, so all my testing revolves around that. I believe I've read that colder water can slow the wash process a little, but I haven't tested my own cold winter tap water for film washing, so I can't really comment.
Others have pointed out that the 'by changes' approach can be pernickety and depend greatly on personal habits and local water quality for success.
I generally live by a mantra of 'bottle instructions will always work if followed perfectly, but may not be best results. If deviating from bottle instructions or mixing own chemistry be consistent and do your own testing to ensure it still works'.
Some swear by de-ionised final rinses: my filtered darkroom water gives perfectly clean negs with just a little photo-flo type rinse aid. Others may find debris on film if they do not use bottled water. Tap water is not a universal constant.