Because you must measure the cell voltage underload.
So it migght be 1.5V in thge DMM, but drop to 1.3V when drawing 10mA.
The mouse probably measures the battery in max load conditions, whenthe LED is operated and the MCU is running.
Probably a short peak of 25-50mA before going back to sleep.
Just an example, last week I repaired another Tektronix with a depleted calibration NVRAM, with the DMM alone it measured 2.9V, so you might think it was OK, right?.
Well, when touching the probes with my fingers, the current was probably just few uA, but that was enough to drop the voltage down to 2.1V, and pressing harder went under 1.7V!