"no one is saying that the sound of Beats headphones is phenomenal. But, bombastic bass and all, they are significantly better than most earbuds"
This is true... But Apple couldn't care less about the headphones. Sure, they may look at them and pinch some ideas, but Apple never had much problem making - what they consider - great hardware. Beats headphones will be a thing of the past in 12-24 months.
On the flip side, Apple have been notoriously bad at making service based systems. All you have to do is google for .mac (pronounced Dot Mac), MobileMe and even iCloud and you'll see the bad press they got over those systems. People even complain about iTunes, although it is a big enough cash cow that they can afford to spend money to fix it.... And that is where Beats comes in.
As you said, Beats Music service is one of the best and has a lot of subscribers, something that iTunes Radio has so far failed to attract. Apple can either build something different but has all that historical bad press about Apple services attached to it, or they can buy a service that is already popular and even fashionable among the demographic they are trying to reach.
They aren't paying $3.2 billion for headphones. They are paying to get a good music service and to use that to erase their poor services record from our memories.