No, not necessarily. Renting just implies you're not the owner and need to follow someone's rules, (that of the actual owner), in order to make use of the rented item.
'Purchasing' a Kindle book or video on Amazon is also renting for example and yet it does not mean you have to continue paying and yet you don't own the copy as Amazon's going to decide how you're allowed to consume it and if they're going to let you keep it[1][2].
I don’t think purchasing a computer is the same thing as buying a movie from Amazon. The computer is always gonna be yours, and you can do whatever you want with it, even if Apple has made it very difficult to do so. But there are lots of objects in my house that would fall under that category as well, but I consider myself as their owner.
