It can also be worse. I'd guess for almost everybody the difference in taste is dominated by the placebo effect.
That Penn & Teller YouTube link even has a section showing this, though you only need to go to the supermarket and look closely at the fine print of all the different brands of bottle water. You'll quickly find a lot are tap water.
I’ve lived in places with tap water that is definitely noticeable vs filtered/treated water. San Jose water for example is extremely hard and I suspect few people would mistake it for bottled.
https://www.wine-economics.org/aawe/wp-content/uploads/2018/...