Source, at around 5:25: Justice John Paul Stevens with interviewer Stephen Colbert
[1.] Some people have different rights than others do.
=> 2. Some people have different rights than others do have different rights.
I guess the meaning of 1 as: 3. Some people's rights differ from other people's rights.
I also guess that Justice Stevens is using verb phrase ellipsis. Yet completion of the ellipsis in 1 produces 2, which doesn't sound correct? So how does 1 mean exactly 3?