MC78M12 voltage regulator without bypass capacitors in a simple PCB with only analog signals
The regulator will certainly not be damaged by leaving capacitors out. 

It will probably work in the situation you describe, but it would be better to have the capacitors on there. 

I suspect you may have miswired the chip (swapped input and output, perhaps) or the chip has been damaged from some previous mishap such as reversed input voltage. 

On a 12V 78xx regulator you should also consider having a diode across it if the input power can be shorted or have a heavy load applied.