That's the part that Google Licenses. You can't distribute their Services and Play because those aren't part of AOSP. That's where you put the hinge.
Yes you can download and install and distribute the OS. However most devices that do that aren't really well received. They tend to be low quality cheap knock-offs. Most vendors that sell Android devices need the Google Services and Google Play on their device and have a license to distribute those "Non-Open Source" components. The cheap vendors that are including these parts without proper licensing (and there have been a few, mostly China) are in violation and open to legal action.