It's kind of true, though - HD and Lowe's are like the WalMart of building materials. Some things (e.g. nails and screws) are standard. For other things (windows, doors, flooring, siding), they sell a narrow variety of stuff that's around or below the bottom end of what's available at businesses that specialize in those things (e.g. Anderson, Pella, Marvin, etc. for windows; Lowe's carries the bottom of the line of Pella, as HD does for Jeld Wen).

The point OP makes about faucets is the most clear-cut difference: HD and Lowe's have the same exact faucet from the same manufacturer but built with inferior internals; the local plumbing supply house has the same thing but with the internals that were originally engineered for that unit. And of course, it will cost more.