That is certainly possible, but I suspect it isn't the case.
In order to get something to you there are a few steps:
1. They have to have it in inventory.
2. They have to package and ship the item out.
3. The courier has to deliver it.
#3 should be the same for everybody, though I'm sure Amazon can negotiate lower rates on the basis of volume and integration (it isn't like the guy at Amazon picks up the phone and calls UPS to ask for a pickup, etc). Also, Amazon can save money by keeping lots of metrics on delivery times. If the USPS gets stuff from zip code 1 to zip code 2 in 2 days 99% of the time, then they can sell that as 2-day shipping and bribe the customers with incentives anytime there is a miss, rather than paying 2x as much for guaranteed 2-day shipping from somebody else (which also has some failure rate anyway).
A large hardware chain could probably achieve #1, but whether they do is debatable. You'd be amazed at how poor big companies can be at inventory management, and historically this has caused many a company's ruin. Walmart killed KMart and everybody else largely on the basis of really well-managed inventory. Dell nearly killed just about everybody else back in the day because of just-in-time inventory management for rapidly-depreciating assets like CPUs (you can't buy a $500 CPU and then take a month to sell it when your competitor just buys it a month later for $400).
However, I think #2 is the real killer. Sears and Amazon may very well have the same product available in their warehouses. However, with Amazon after you click the button they may very well have a robot with the item heading to the packing line in 15 minutes, with the shipment data already transmitted electronically to their carrier. They are extremely efficient at getting stuff out the door. An item that somebody wants to buy and which is sitting on your shelf is just a waste of space and money, and customer satisfaction as well.
In my experience that is where most companies fail. With Amazon if I buy with 2-day shipping the thing is out the door same day before 5PM or whatever (and that cutoff is very late in the day compared to many competitors). With Amazon 2-day means that I have the item in 2-days. With most other big vendors if I buy with 2-day shipping it often means that they take 3-4 days to ship the thing out, and then it arrives 2 days later. So, I'm paying that premium on shipping just to watch the vendor fumble around with my order, and I never really am sure about when it will arrive.
Amazon is pretty ruthless on this stuff, and IMHO their practices are so ruthless they border on human-rights violations in their actual warehouses. However, even if they cleaned that stuff up they'd still be way cheaper and faster than just about anybody else. Companies that want to compete have to invest a lot more in streamlined processes, because customers aren't going to pay for mail-order that takes a week to arrive.