If you can buy a new phone for $5 and the referral bonus is $20, there's $15 arbitrage to be made just by buying up as many phones as you can.

So I think their goal is not so much about identifying people, but identifying devices in order to prevent this loophole.

But can you buy (even a stolen) iPhone for USD 5?

The question is, can you buy it and sell it again with less than a 20$ loss

Yup, no question. I'm not claiming Uber's approach is flawless, I'm just describing what I believe they were doing and why.