This isn't just hypothetical: for a while I was using QFC (Kroger) for grocery pickup, but after one too many instances of adding an item to my cart and then only finding out at checkout that a third of my items weren't actually available, I said to hell with it and switched to doing all that at Whole Foods instead, since their inventory counts are actually correct.
A. [explicit claim; humorous] Analytics confirm that, if you show people whether products are in stock locally, they won't buy those products on your website.
B. [by implication] This is bad, because it "lowers" your sales. So you can't display this information.
C. [by implication] The retailers are making a mistake - the reason people don't buy products on the website when availability information is displayed is that they go to the store and buy the product there.
D. [summing up] If you measure something you don't care about, you will end up doing things that make you look like an idiot.