Municipal and well water (drinking water) are tested, and required to meet specific levels of purity. Mycobacteria is not one of the pathogens tested for because it is everywhere in water, soil and air, and most people are not adversely affected by it.

That leaves those vulnerable to infection to figure out how to best get the pure water they want. So here is a little tutorial on these terms:
Drinking water
Purified water
Filtered water
Distilled water
Sterile water
Spring water

There is no standard for "purified" or "filtered" water in the US. Most purified or filtered water comes from municipal water supplies and is bottled in plants that are only concerned about safety (as in no e. coli) and clarity, so clean techniques are used, but not necessarily sterile. To be free of mycobacteria filtered water must pass through .2 micron filters - I'm not aware of any bottling plant that does this.

Distilled water is processed into steam and then returned to it's liquid state. It is sterile after the process, but if it is not bottled under sterile conditions, may become contaminated as well.

Sterile water, such as the liter bottles used for cleaning wounds, is sterilized by boiling or distillation, then immediately bottled under sterile conditions. Once opened, it is used on a single patient and discarded after 24 hours.

Spring water comes naturally to the surface from underground, and is required to be bottled in such a way as it does not become contaminated. Dr Joe Falkinham and his students have tested many brands of spring water and found them to be free of mycobacteria.

Tap water may be treated at home to make it free of mycobacteria. It may be boiled for 10 minutes plus 1 minute for each 1000 feet above sea level or it may be passed through a .2 micron filter. In either case, it must then be stored in sanitized containers.

Tap, filtered, purified and spring water may still contain dissolved solids (generally minerals) which do not mean it is unsafe.