I disagree with your disagreement. In the common layman's mind, if you "purchase" something, then the company should not be able to take it back from you.

Especially since it's not like Apple is guaranteeing that you get to keep the product for a minimum amount of time. They could just as well delete your purchase a minute after you bought it.

There isn't a single human on planet earth who thinks of such a transaction that gets withdrawn after one minute as a regular legitimate "purchase" of a product. Even "rental" doesn't quite cut it, it's more in the land of "fraud".

I'm not sure we can equate deleting a purchased digital asset with taking back a physical item. I'd imagine deleting something would be more akin to selling a product that is designed to break after a certain amount of time.

There's a pretty wide variance of what people consider acceptable from purchased things, e.g. People generally accept the idea that a mattress will eventually need to get changed even if it comes with a lifetime warranty.

Actually, intentionally designing a product to break after a certain time is planned obsolescence and is not accepted at all.

Note that this is not about Apple taking content back. It's about Apple not allowing content to be re-downloaded after it has been deleted locally, if it has been pulled from the iTunes Store in the meantime. We're an all-iTunes household, as are my parents and in-laws, and the fact that iTunes "purchases" are subject to this condition has never elicited a comment from anyone I know.

Well, there's one thing that could show the difference. If it's a true "purchase" then the first-sale doctrine, [1], should hold, which limits the rights of the copyright owner.

[1] https://en.wikipedia.org/wiki/First-sale_doctrine

A "sale" is a necessary pre-condition to application of the first-sale doctrine, but that does not imply that exhaustion of copyright is a necessary pre-condition to the existence of a "sale." The Copyright Office's official position is that first-sale doctrine does not apply to digital sales, not because they are not "sales," but because they necessarily involve creating a copy of the digital item--unlike the sale of a physical item. The Copyright Office and USPTO has stated that digital sales do not meet key assumptions underlying the first-sale doctrine: there is no tangible good that can be owned by only one person at a time that is subject to wearing out.

"Lease" or "License" would be less deceptive terms. The FTC should prohibit "Purchase" and "Buy".

You purchase a revokable license, since it's a one-time payment, not subscription, and since it's not a product you are purchasing.

The whole value proposition is unlike anything else. Why not use a new word. The market freely adopts new words, like freemium, hire-purchase, in-app-purchase etc.