The real issues are related to the anti-fragmentation clauses. If you sign the MADA agreements, you can only do the full certified Google android. You cannot put out a standard android device also. You must certify every firmware load with an agent of Googles and pay for the privilege. It also means you cannot use third party services to replace Googles. Their agreements are totally anti-competitive due to locking you in and locking other options and vendors out.
As explained by other, there are actually two Android OS. The AOSP (Android Open Source Project), the one that is open and available to everyone, without restrictions nor contracts nor agreements. Then there is Google Android, i.e. Google customization of AOSP. The difference is exactly in the Google branded apps: for example mail app in AOSP is open source and generic, while in Google Android is the Google branded Gmail app (not open source). The same for Camera app, search bar and so on.
If you want to ship a phone with PlayStore officially installed, you have to sign MADA agreements to be allowed to ship a Google Android OS. Else, if you don't want to sign agreement, you can ship an AOSP (like CyanogenMod) without PlayStore, but users can still install separately Google Apps and PlayStore (legal, but quite difficult, not for everyone).
So, AOSP is fully open, Google Android is not. Hardware vendors prefer to sign for Google Android because they WANT Google ecosystem, else they would have to fork AOSP like Amazon with Kindle or Nokia with Nokia X, and create thery own app store.