A sibling post about beer is also interesting. Beer kegs are owned by the brewery -- you buy the beer inside the kegs and you must return the keg. However, it is common for (very) small breweries to refill kegs that aren't theirs. If you buy a keg of beer from brewery A, drink the beer, take the keg to brewery B and ask them to fill it, they often will (if they have time).
Usually, there is a clause in the agreement with the brewery that owns the keg that you will not refill it. However, that's a contract with the customer, not the competing brewery and as far as I know, it is not illegal for the second brewery to refill them (but the customer can be sued).
Let's say the original brewery has a patent on the keg in question. Normally you would not be able to use the keg because you do not have a license to the patent. I think the interesting point here is that if the original brewery retains ownership of the keg, then the second brewery can not refill the keg without infringing on the patent. However, if the brewery sells the keg to the customer, then the customer sells the keg to the second brewery -- the patent is exhausted (in the opinion of given in the link). So the brewery can fill the keg because they own it.
To be honest, while I think a sane law would work this way, I'll bet this is trickier than it seems. Let's say you have a special filling mechanism on the keg that is patented. You can sell the keg to the user. The user can use the keg for it's intended purpose (to dispense beer). The user can then sell the keg (either full or empty) for its intended purpose (to dispense beer). However, they can explicitly say, "We do not transfer the patent rights for filling this keg using our patented filling system". The user signs an agreement stating that they understand that the keg can not be refilled and that they have not bought the rights to the filling system.
In that case, when they resell the keg, how can the patent rights be exhausted? The customer never bought them in the first place.
So I expect SCOTUS will rule against this (unfortunately).