I think you're being pedantic. What I wrote is true for
purified bottled water. The FDA link says "Municipal water is usually treated before it is bottled." and then "water that has been treated...may meet standards that allow it to be labeled as “purified water.”".
If you believe that bottled water is less clean than tap, then only one of the following must be true:
1. The sourced municipal tap water is already purified such that any additional treatment does nothing.
2. The bottled water in question is not labeled as purified (and is not from a spring, well, or other non-municipal source).
A quick internet search reveals that all the major bottled water brands are either explicitly labeled as purified municipal tap (Smart Water, Dasani), or excluded from the discussion because they are from a spring or well (Evian, Arrowhead). I have yet find a single brand of unpurified non-spring water. However, I did learn that all bottled water regardless of source must meet the U.S. Pharmacopeia 23rd Rev. standards (which are unfortunately paywalled).
It seems unlikely you'll encounter unpurified, straight-from-the-tap bottled water, striking conjecture #2 from the list. Therefore, if conjecture #1 is true, then the only thing that can be said is bottled water is at least as good as municipal tap, but never worse.