If you look at the diagram for a full bridge rectifier it will be apparent why it tests open on the 'AC' side. There is no path for DC, it is like a bunch of valves that reverses the connection on each mains cycle.
I think the problem is that COM on a meter is not the same as battery ground, it is going to be floating at some midpoint reference. Maybe 3V for instance. Then the ADC can measure voltages above and below COM potential.
If what you did is to either short COM to battery ground, or to +9V, then it's very likely that the reference will have been damaged.
Unfortunately on many meters this reference does in fact come from the main ASIC.