There were two helicopters involved, border patrol and tucson police. They also phoned into the FAA as it was going down.
They also made visual contact with the light on the underside of the drone: "From what I can tell just from its position light, you know, I would have to imagine it was larger than a quadcopter"
It's not necessarily that they can't, it's that the precision in altitude is very poor unless the target is close to the radar. This happened with MH370, the data released in the investigation shows altitude values varying wildly by 10000 feet in a short time. Of course conspiracy theorists picked up on that as proof of lizard people involvement.
No commercial aviation radar system even tries to output non-transponder altitude infomation. Many are secondary only and don't even pick up targets without transponders.
Military primary radar, like the one that picked up MH370, obviously can.
But I don't think any of those are designed for really accurate altitude measurements. That job is usually done with targeting radar which (at the expense of not being able to see multiple targets) can lock a single target and get it's exact position.
We should be long past the point of uncritically believing everything police claim.