It's true that local stores can have the same water, but that doesn't mean much of anything once you're talking about established tanks.
For example, if your LFS is very serious about constant fresh water and cleanliness, chances are their water will be little changed from its original source parameters. Some LFSs are serious enough to use new water almost daily.
But your tank might be well established and you probably don't change the water daily. That means you might have some softening and more acid.
And in my case, I have blackwater tanks. I'm taking fish from often high alkalinity LFS water and putting them into below neutral water.
Not to mention that just because it's a "local" fish store that really doesn't mean they have the same source water. For example here in Philadelphia we have three plants as tap water sources. Two get their water from the Schuylkill River, which has a higher mineral content and is slightly harder than water from the Delaware River. The other one gets it from the Delaware, and serves not only parts of Philadelphia but also parts of Bucks County.
That means your friend who lives across the street might be getting their water from a different plant. Same goes for an LFS.
Not to mention if you live in a more rural area, the sources of tap water can be all manner of wells, aquifers, springs, etc. Three or four different sources may be found within only a square mile.