I disagree with you both, although this could be because I have a UK perspective on the issue. Over here, you can either buy "locked" phones, which typically come with a pay-as-you-go sim. Regarding these, I basically agree with you, the network has subsidised them heavily, so they're not really "your" phone.
On the other hand, you can get phones on contract. This involves signing up for a specified number of months, and possibly paying something up front. In this case, you're buying the phone, however you're essentially buying it on credit and paying it off over 12-24 months. In this case (at least over here) the phones generally come unlocked, so you can move to a different network if you wish, but you'll still have to pay your contract's monthly fee, even if you don't use the network.
In the latter case, I feel it's perfectly fair to consider the phone to belong to the customer. They've paid for it, and the service.
The other difference between the US and the UK is this ridiculous notion of crippled phones - over here, they might sometimes be locked to a network to cover the subsidy, but I've never had one which has had features deliberately disabled by the network which is what preventing you rooting the device basically amounts to.