Sorry, that's my fault, I was editing my comment to make it more concise but managed to also extract its clarity. :)
I would agree about Italy and Spain. At least in Italy, many restaurants provided some regional brand of mineral water from a local-ish spring, but I virtually never saw someone asking for tap water.
In the US, I would even be surprised if I asked for water and was brought a bottle that I would be charged for, although I'm sure there are places that will try and up-sell bottled water.
In Switzerland, there's something of a dichotomy in my experience. In homes and most public spaces, including self-serve restaurants that often have a filling station, tap water is almost always the expectation. It's also much more accepted to drink directly by putting one's mouth up to a tap, whereas in the US I imagine most people would find a dedicated water fountain, cup, bottle, etc. With waiter service, however, there seems to be at least a weak expectation in Switzerland that a patron will order some beverage. Asking for tap water didn't seem frowned upon, but I would get noticeably more hesitation for it than anywhere I've been in the US or Canada.
EDIT: Minor rewording for clarity.