I'd still need some proof of that.
Big box stores can dictate the price they'll pay, but that's not the whole story.
Costco, for instance has items that look identical in every way to the same thing at Best Buy, but if you look closer, there is a one digit part number difference and the only place that number can be had is from Costco. It's not the same part. Lowe's has their own brand of tools, Kobalt, and their own brand of ceiling fans. Can't compare them to others. Home Depot generators and Costco safes can have a different part number and look identical to others.
But if the part number is the same, I bet the item is the same.
I've even been told that redimix concrete in the identical package from the same manufacturer is not as good at HD. Really?
I'm not sure it's true and I don't know how to prove it.
On top of that there is a lot more to pricing than subtle differences you can't see. Boutique stores can charge several times more for stuff that is absolutely no better and they can be hard to deal with when it's time to get parts or return something.
I have no problem dealing with big box stores. You can pick up and look at a large selection of stuff and pick what you want. You can go in and figure out how to make something work by looking around. And no matter what you get, as far as tools at the big box, it's probably many times better than a Harbor Freight tool, especially their electrical "tools" and yet people flock to Harbor Freight to buy tools. Go figure.