Classics Battery Holder vs. Battery Pack

[AndiGer]

Inspired by Mark Hoskin's battery holder for classics that take 3 AAA cells I built one myself.
But when I put it in an HP-67 with even freshly loaded AAA batteries that give together 4.1 V I get the low battery indicator on (650 mAh or 900 mAh cells, doesn't give a difference).
In contrary I lately re-designed a cell phone battery pack with 3 AAA 800 mAh cells in it and the low battery indicator does not appear also I measure only 3.95 V.

What is the difference here? Why do I get the indicator on using the holder but not with the pack? Different current flow given to the calculator?