I think there's a few possible angles here.
* Cheap and Expensive as a subjective thing. Paying a $10 per month fridge bill in perpetuity may feel less uncomfortable than the sudden expense of a $700 fridge every 8 years, even though the latter is cheaper.
* A service can take some of the bad-decision factors out of it. Many appliances are panic-bought when the previous unit fails, rather than waiting for the price to bottom out. A predictable lease price and service organization avoids that risk. It might not be as cheap as the cheapest unit on the best day, but it's competitive with a mid-line product.
* The rental service product could benefit from economies of scale and standardization that direct-to-consumer brands don't offer. Whirlpool sells a few dozen different 25-cubic-foot fridges, with constant model churn. Any given model may only have a total run of a couple thousand units. Fridge-as-a-service may only offer one, and offer it for 10 years, allowing slower amortization of engineering costs and less expensive service/spares management.
* A structured end-of-life program could bring down the cost of leasing. After five years, they swap out the old fridge, but then they can refurbish it and either return it to the lease pool or resell it in a less ad-hoc manner than listing individual units on Craigslist.