Batteries are decently complicated devices. They're certainly more complicated than an ideal voltage source. As you've noticed, we often model them as a voltage source with a series "internal resistance." This is a better model which works well in a large range of conditions, but still not a true model of how batteries work.
When you short a battery out, initially you do get the very high amperages you calculated. However, as the short continues, chemistry gets involved. Inside the battery you have two materials reacting with each other to provide the electrical energy. In the case of your example battery, NiMH, the reactions are:
Negative terminal: $H_2O + M + e^− \Leftrightarrow OH^− + MH$
Positive terminal: $Ni(OH)_2 + OH^− \Leftrightarrow NiO(OH) + H_2O + e^−$
Noe that the negative terminal produces hydroxide ions and the positive terminal consumes them. Also note the double arrows on both equations. The equilibrium point depends strongly on the concentrations of the compounds.
In normal operation, the hydroxide ions have time to work their way from the negative terminal to the positive terminal, keeping the reactions going smoothly. However, in a short, there will be a build up of hydroxide near the negative terminal because it takes time to diffuse away from the terminal. This will reduce the rate at which the reaction occurs, reducing the maximum current the battery produces in this short example to below what you would expect from modeling the internal resistance alone.
Also, depending on your battery, there may be 3rd order effects. You're going to generate lots of heat in the battery, and that causes reactions to change rates. Depending on the battery, this may accelerate the discharge. For an example of what these effects might be like, I point to this video of a lithium-ion battery. In this case the battery was *ahem* "encouraged" with a knife, but runaways like this for lithium ion batteries are not unheard of.
