In the beginning, there was Android. Android was an open-source, largely hardware-agnostic operating system designed to work on a variety of devices and form-factors, and then Google bought the company that made it (also called Android, founded by Andy Rubin). Then, there was Google's Android. Google's Android was still open source, but now it came with stuff you'd actually want to use. Like an app store. And Google Maps. And Gmail. And Google Search. And did I mention Android itself was and is still open source? Because it was and is, and will continue to be likely for many, many, many years into the future.
Google, in the interest of avoiding fragmentation in this nascent operating system / ecosystem, founded a group called the Open Handset Alliance. If you joined the OHA, you got access not only to the same Android source code everyone else did, you got access to unreleased versions of it earlier, as well as the ability to submit your handset products to Google for certification (via the CTS and MADA agreement) so that they could have this very-desirable suite of Google apps, plus the Android Market. Did I mention this was voluntary? It was voluntary. It's still voluntary. It will continue to be voluntary.
If you don't want to join the club? There's no problem: you don't have to. You can take Android and do literally whatever you want with it. You can even compete directly with Google - that's kind of the whole point of the open source thing. But, if you are a part of the OHA, you agree to do exactly not this. Because this would be tantamount to, say, being a Windows distributor and then simultaneously selling products with a reverse-engineered, incompatible, de-Microsofted version of Windows as your own on the side. It would be, as one in the industry might say, a pretty piss-poor business model. To put it bluntly: you can either do Android with Google, or you will be doing it without them. And that's fine: people saying there is a problem with this are basically upset that Google has coercive power over OHA members that have voluntarily chosen to be a part of an organization with rules. All of those members are free to leave at any time.
Today, Bloomberg is reporting that the FTC has heard these people yet again and decided to conduct an investigatory probe in cooperation with the Department of Justice, the subject of which is, you guessed it: the legitimacy of Google's practice of bundling its apps and services with Android as a requirement for handset partners who are OHA members. The only goal of which, if the FTC decides to pursue a case, would of course be to discourage Google from bundling these things, which would pretty much eliminate Google's entire business incentive for starting the OHA to begin with.
And the reason there's this special "Android OEM club" to begin with? Because Android would be a total fucking mess without it. Look at Android in mainland China. That's what you get without the OHA. Tons of malware, insane app piracy rates, phones that often rarely get OS updates, are riddled with security flaws, and generally exist in a wild west of computing in which fragmentation is only limited to the extent necessary to ensure popular applications will actually run on a given device. Many of these devices, by the way, still have plenty of closed-source software preloaded on them doing who knows what and sending your information who knows where, and the companies making these phones are accountable to basically no one and, even if they were, would just fold up overnight and reemerge with a new name a few months later or will simply have the market fill the void. I'm not saying "Google's Android" has none of these problems, but I am saying they are exponentially exacerbated without the rules and controls of the OHA. You do not want a non-OHA Android.
And so, there is an exchange of value between Google and phone manufacturers. Google gets to preload its apps and services on phones, manufacturers agree not to do certain things with Android, to meet performance and general compatibility requirements, and to not run off and build a competing non-Google Android while simultaneously profiting off of Google's apps, services, and ecosystem. It seems like a pretty fair trade because it is: phone companies generally suck at software and services, and Google provides many of us some pretty massive benefits by building those things. The beauty of "Google's Android" is that we have a largely compatible ecosystem of devices that can run the same applications and services, and we receive the benefits of the larger Google umbrella: an app store with malware and other protections, accessories like Android Wear that work with a huge number of Android phones, the ability to easily switch between devices, reduce OEM lock-in, and probably a half-dozen other reasons that I'm not even thinking of right now. Basically, the OHA is good. For any "bad" product of the OHA's structure and rules (which I am not saying are gospel - merely that they have been good for Android and us as a whole), there are benefits that outweigh them to such a degree it's not even funny. And let us not forget: no one with an Android phone is forced to use any Google services, though it obviously is preferable to do so even from a strictly functional perspective. The Amazon Appstore exists.
Joe OEM can go build an Android phone tomorrow without the Play Store, preload Amazon's Appstore and whatever the hell else they want, and put it on sale. Now, Joe OEM could not also simultaneously sell a phone with Google's Play Store, but that only makes sense - you'd have Samsung and LG and every other OEM that only uses Android because of its marketability and popularity trying to sidestep Google constantly, which would just make an utter mess of the smartphone market. We do not want that. No one wants that.
So, what's the FTC's "problem" with how Google handles bundling its services with Android? I don't know (apparently it's the hip thing to do right now, though!) - I just know it probably stems from a deeply misguided view of what Android actually is.