What could cause unexpected high water usage?
Finally resolved this one.  It surprised everyone.  The apartment had a HW Expansion Tank (required by code) but no check valve (the building has one, but individual units don't).  

It turns out water was flowing through the meter into the HW expansion tank, then flowing back out - no net water consumption, just a few ounces of water cycling into and out of the expansion tank with changes in pressure. 3,000 gallons a month is about 9 ounces a minute.

But the water meter only advances in one direction, so it accumulated as usage.  We installed a check valve and the problem was corrected. 

Wow.