To keep George company I checked shortcut current for a bunch of batteries I've got in the drawer.
Rechargeables: 2500 mAh Eneloop Pro - 4.9 A, 2300 mAh Energizer - 4.6 A, 2000 mAh Energizer - 4.6 A, old 1900 mAh Eneloop - 4.0 A.
Alkaline batteries: Duracell - 4.2 A, Kodak Extra - 4.1 A, Panasonic Essential - 3.8 A
The main conclusion is that George has better leads on his multimeter than me
Ohm's Law R = U/I tells us that the combined resistance of the multimeter and the internal resistance of the battery is between 0.24 Ohm and 0.32 Ohm in my case. About 0.22 Ohm comes from the leads and the rest 0.02 - 0.10 Ohm is the internal resistance of the battery. The results are consistent with other sources:
http://www.learningaboutelectronics....nal-resistance
In other words, if it was not for the leads, the shortcut current could of been about 50 A. There are videos on youtube of people short-circuiting batteries with a paper clip to start a fire.