Apple cannot update without carrier interference. Apple, however, does things differently enough from Google that the carriers have a better opportunity and more willingness to play ball.
Apple releases operating system updates once or twice a year, tops. They have a customer base who (by and large) values stability over the latest features. So iOS is released to the carriers months before it needs to be rolled out to the customers, with a clear deadline dictated by Apple.
Apple also has a large customer base at any carrier they choose to do business with, all running a very, VERY small selection of phones that need to be updated (usually the last 3-4 models of phone at most - ignoring the various memory sizes). So once the code hits the carrier, each carrier has four specific phone models to build the implemented version against, and the build is largely adding radio drivers and any other special sauce they feel they need to add. So carriers can make and test builds for all relevant models in a matter of a few weeks, and they have months to accomplish it.
Compare that with Android:
1. Deep fragmentation in hardware from many manufacturers with differences in hardware, including the cell radios.
2. Updates have to come from Google, then hit the phone manufacturer so they can add their hardware drivers for their screens, cameras, etc and their custom launchers (Touchwiz, Sense, etc). Then hit the carrier for addition of radio drivers (for non-GSM/GPRS/EDGE/HSPA+ radios) and bloatware.
3. Google releases updates to the OS to AOSP every few months.
If a carrier takes on the iPhone, they are taking on a commitment to assist in crafting one update for maybe 4-5 phone models once or twice a year. In return, they get a customer base that can often account for half their smartphone customer base or more. It's MILLIONS of almost guaranteed new customers for a small commitment.
As far as Android, well, one does not simply walk into Mordor. If a carrier wants to carry Android phones, chances are they'll have at least two or three competing Flagship models at any given time, each requiring frequent updates that will be different from each other, coming from different manufacturers on different release schedules, using different radio drivers from model to model. Flagship status will move from phone to phone several times a year, and you'll have at least 2-3 of them at any time, so if you look at just the "Flagship" phones you sold in the last two years you're looking at a minimum of 15-20 diverse models from at least 2-3 manufacturers, each with their own UI you need to accommodate for in your build for that phone.
The ideal answer, of course, is for the carriers to either adopt cell radio standards or at least publish open drivers for their proprietary networks. T-Mobile, AT&T, and others have adopted GSM and implemented it plain-vanilla as per standard. So any international-standard phone that can adapt to US-assigned GSM frequencies will work seamlessly with AT&T, up to but not including LTE. Search Amazon for "unlocked AT&T phone" and prepare to get lost in a sea of third-party-built phones that AT&T will happily accommodate on their network. Buy one, pop in your SIM, maybe make a few APN changes so the phone learns how to turn on data, and Bob's your uncle.
Sprint and Verizon have chosen to keep and in fact complicate their proprietary networks (Verizon actually has a specific 3G/CDMA protocol for the Thunderbolt and Rezound that allow them simultaneous voice and data over 3G - no other phones on the Verizon network I'm aware of use this protocol). In order to put a phone on their networks, you need to involve them. Not just from a manufacturing perspective, but phone-by-phone. Search Amazon for "unlocked Verizon phone".
Nexus phones have a chicken-and-egg problem. Until sufficient people start demanding Android and frequent updates, the carriers don't have any incentive to put that much effort into frequently updating dozens of phones to get relatively few customers per phone, or opening up their networks to phones they don't HAVE to support. And unless the carriers open their networks up or commit to frequent updates, customers will look at phones like the N4 and say (quite understandably) "No LTE? No CDMA? Pfffttt.. useless niche toy."
My next phone will be a Nexus. Of necessity, then, that phone will be GSM and probably not have LTE. And that's fine by me - I value frequent OS updates and the latest features over absolute stability and the fastest network speeds. For the forseeable future, we will be in the minority. And I honestly don't care, because I can now buy unlocked phones for the same prices all my friends are paying with 2-year commitments, and save money month-to-month by buying contractless prepaid plans and "carrier hopping" to save money if I choose.
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