1st:
Android isn't successful because it's open but because it's "end-user friendly" (whatever that means - most people can use it intuitively).
My father is a good example for this. He has a Galaxy S2 and has what is usually called "advanced computer skills": He can maintain his Windows PC, is clever enough to avoid the common PEBKAC problems and in theory knows how to code. But he hasn't coded himself for more than 20 years now, so he couldn't care less about his phone's operating system being open source.

2nd:
Google frequently fails to deliver the source code as required by #2 of the open source definition [1] and has to be reminded very often to release it.
Also, even though it's not strictly a failure in terms of the OSD #2 & #3 since these paragraphs only refer to the license Google's Android is (or at least has been in the past when I checked) technically designed to make derived works hard without ripping the whole system apart and putting it back together from scratch. For example in Android 2.2 it was not possible even on a rooted phone to load additional kernel modules simply because the /system partition where these modules HAD to be stored had virtually no free space left. Resizing the partition was not possible due to automated integrity checks that complained about wrong partition sizes.

bottom line:
Yes, strictly spoken Android is open source by the terms of the OSD once they released the source code. But if you don't go by the definition but by the spirit of open source Android is not open. Google only makes it as open as is required by the licenses they are obliged to respect. Unfortunately this kind of openness is worthless.

[1] http://opensource.org/docs/osd