Shipping a generic Android on their platforms would have been possible, and also entirely uninteresting. The phone market isn't interested in unskinned Android. Asus, meanwhile, have been shipping Android tablets for over two years.
There's simply no way Nokia could have shipped an Android device as compelling as the Lumia in 10 months. Tying themselves to Windows gives them a chance of market dominance rather than guaranteeing gradual irrelevance.