My first thought was "nah, that doesn't make sense." Don't Fear The Reaper has a very simple, repetitive melody. Aside from that one (sick) solo in the middle it's a very predictable song at an upbeat tempo. Easy to listen to, easy to picture in your mind. The sheet music I've found supports this. The backing track here is actually incredibly simple. The vocals a little bit less so, but they're not that difficult.
Then I started thinking about what songs I know are similar to this. And that's where my theory fell apart a little bit. One of my personal favorite songs,
Mayday by Flobots does this too. It's not even my typical genre; I'm usually more of a metalhead. But the actual backing track is very easy to listen to, the vocals are interesting, and the chorus literally is two people talking over each other.
Then I thought, well, Don't Fear The Reaper has a very heavily syncopated rhythm in the vocals. The singer tends to interrupt himself on beat 2 of a measure, which is a weak beat. How is that reflected in Mayday? The answer is that it's not reflected at all. Lines start on beats 1 or 3 and last 2 beats. So, I guess they're snazzy for different reasons? What else fits this?
What if I look for similar patterns between a singer and an instrumentalist? What songs could mimic this type of cutting off pattern between voice + guitar, for instance? Octavarium's
Panic Attack kind of does? (By the way, it's kind of a rule that everyone either has listened to this once or is going to listen to this once. Do your duty if you haven't already.) During the verses you have an action where the guitar is silencing the vocalist, but you're kind of pushing the envelope by considering this anything other than a call and response.