How reassured (typically that is) should one feel about the possibility of a heart attack after receiving a negative nuclear stress test result?

Not perfect. It is reassuring but not perfect. The nuclear study relies on differential distribution of blood flow and the dye. Most CAD show distribution in vessels unequally, therefore, the dye will be distributed unequally. If there is diffuse disease, the distribution could be equal and will miss the differential and will read as no disease. Talk to your md or cardiologist if in doubt of symptoms.
Nuke. A normal perfusion study predicts a low probability of heart attack over the next year or two. You should discuss your specifics with the doctors who know you.