No, if you want to keep it formal - it's not a purchase. It's rental. But since it's presented to people as purchase, people should treat it as purchase. And don't claim that people who buy it are buying any "rights" (i.e. keeping in mind to buy some abstract "rights"). They are buying content.
There isn't a dichotomy between rent and purchase. In both cases, you're buying a bundle of rights with respect to somemthing. You may buy use of something yet be restricted in that use. Consider buying a condo. You "own" the condo, but there are all sorts of restrictions on what you can do.
The real question is: are people aware of the terms of the deal? Are the aware of the specific rights they are purchasing when they buy DRM content? I think they are.
Dichotomy is in perception. Rental can be formally called "buying rights to use it for limited time". Still there are two distinctly perceived use cases (even if not fully formal) - "buying" and "renting". Buying implies owning it, renting implies limited usage (not owning it). Distributed content is presented to people as "purchase", while DRM attempts to limit the use case to "renting". It's misleading and unfair. As long as it's presented as "buying", people should treat it as buying.
Explicitly presenting it as "renting" decreases the attractiveness, that's why DRM inclined distributors mislead their users with avoiding the usage of the "rent" term. But it only strengthens my point - since they rely on implicit perception of buying to attract people, people should treat this interaction as buying and these distributors should not complain when their DRM is scraped.
A lease and a purchase are legally distinct concepts. Generally, a lease is a time-limited acquisition of rights. A purchase is an unlimited (with respect to time) acquisition of rights.
A license can be purchased, even if it does not carry all of the rights associated with the underlying product. A license can also be leased, in which case the license is of a limited duration.
A purchase of a DRM-protected good is a purchase of a license to use an IP on the condition that the usage is subject to a rights management policy. This is not a rental, because the license is not time-limited in the acquisition agreement itself. (Thus, even if the DRM servers were disabled the next day, it would not have been a lease--the terms of the acquisition agreement itself are what matter.)
Renting does not have to involve a lease, as in being time-limited. Renting can be open-ended.
The key differentiating characteristic of renting vs buying is that in renting ownership of the expected good has not changed or has not fully transferred.
When you buy a good, legal ownership (whatever that means in any given jurisdiction) of that specific good has been transferred in full.
Entities using DRM are exploiting not the ownership transfer but the expectations for that good. The corporate, as it almost always is, transfers ownership of a substitute good which requires a license/renting to access the expected good.
The end users therefore have not bought the expected good, but a substitute good plus an access license "option". With DRM, this "option" can be (technically or legally) revoked or is callable at any time thereby disabling access or removing the expected good.
So, the obvious solution is not to buy a substitute good + callable option when you actually want the underlying (expected) good. Otherwise, you are just creating demand for substitute goods and all the fancy methods to create the callable options.
Ownership does not have to be "transferred in full" for something to be a purchase. They key difference with rentals is the lack of time limit or reserved right to revoke the license. The fact that the purchased rights may be fragile does not make it a rental.
I can sell you an easement on my land. It's a purchase, not a rental. But it can be a very limited right nonetheless (e.g. Just the right to cut across the grass to the road). I can sell you a car on the condition you don't repaint it. I can sell you a piece of land on condition that you only use it for a certain purpose. These are all purchases within the common use of the term, even though they effect a partial transfer of rights.
The discussion above is not about formal definition, but about common perception. Common perception of buying is getting full ownership. All other cases are far less common.
In general, the whole notion of attempting renting the content obscuring it as a sale is not a honest way of doing things. And using DRM to enforce those rental limitations makes it even worse, since it uses unethical preemptive policing methods to do it.
If this is not a time limited acquisition of rights, then what about all the "time windows" and potential revocations? If they exist - it means it's not unlimited in time and therefore it's similar to the lease (of the content), rather than to a purchase.
That was my point above - when people buy, they don't care to buy any "licenses". They buy content. Those who sell it, fool them with selling a license, while making them think they actually buy what they want to buy (i.e. the content). I.e. in essence they lease them the content, while making people think they buy the content.
> If you bought it, you should own it.
If the "real" meaning if the transaction is "rent till we decide you can't anymore", then it shouldn't be misrepresented as a purchase.