That's what I'd heard, that soil organisms will grow better with a source of fixed nitrogen. The nutrients also encourage plants to root there, and those roots force the wood apart. It does seem to me that stumps treated with potassium nitrate do rot faster than otherwise. But, the real reason potassium nitrate was used is different however -- years ago, you saturated the stump with nitrates, then saturated it with kerosene, then lit it. The nitrates provided oxygen for the buried kerosine and wood to burn. Most labels don't suggest this step any more.