Seems to me that both contacts in the tailcap would have to be negative. I'll guess that there's a negative contact at the top of the battery holder as well as the positive. That's the only way I can see for this circuit to work, since there don't appear to be any unanodized body parts to complete the circuit.
No, sorry the center is positive.
This photo of the battery holder shows there is a center metal post.
The electrical contact is made by the body tube end, and the part of the tailcap that meets it - which are both bare metal and unanodized.