The difference between renting and purchasing gets murky (sure, not literally) when you are dealing with sensitive hardware that you rely on but cannot maintain yourself. Such systems usually require frequent maintenance by the supplier. Sure, you could end your maintenance contracts, but then the systems you have purchased will very rapidly become useless. The up-front cost of hardware is often very small compared to the ongoing cost of maintenance contracts, and so the relationship ends up looking a lot like rental.

The parent comment mentions that Delta rents their airplane engines. I imagine that they have the capability to do general maintenance on the engines, but that the engines need to be periodically sent back to the supplier (probably GE or Rolls-Royce) for a teardown, safety inspection, and rebuild. Without regular inspections an engine can't be flown, and is essentially worthless. Not much point in actually owning the engine if you can't use it.