In many cases, bottled water is coming from a municipal water source. It's treated and filtered the same way all municipal water is. About the only thing that happens is that the companies sometimes re-introduce minerals to enhance the flavor.
Bullshit on your bullshit.
It is completely intellectually dishonest to the point of a LIE to assert that water delivered via a sterile, new, plastic container is the equivalent of what runs through the often old, sometimes lead, sometimes infused with bacteria and sediments stuff tossed through underground lines prone to breakage and then on premise, subject to the neglectful landlord's, and cheap ass developer's habits.
You never had the fire department flush their lines and all of a sudden your water is brown for a day? Try shaking a bottle of bottled water, if it becomes brown afterward I'll concede the piped in water is the same as the bottled stuff.
Water from the tap may be "as safe" but it is NOT "as good" most of the time. How come I can go to my neighbor's apartment and the water tastes different? How come the water at the office tastes like there's a goddamn garden hose in the loop somewhere? (Probably because there IS somewhere. ick.)
The water delivery to the tap is completely different, and it's different in a way that's old, broke down, and full of flaws to the point that many consumers routinely filter it to make it semi-palatable again.
That's not "about the only thing that happens". Lie, lie, and then LIE again.