well i think i got the point of what you are talking about the pivot problem. actually you can ignore the pivot point thing when using rigid body since maya calculates the collision and the reaction for you.
this is totally different from keyframing a vase, the point is that you cannot animate pivot point in maya. you can just keyframe the obj by translation or rotation in order to create the illusion of "changing pivot point".
for example a 45 degree clockwise rotated box is going to hit the ground, one edge or corner will hit the ground first and reaction force comes from that side making the box rotate in anti-clockwise direction. at that time the pivot point is somewhere near the centre of the obj.
while the corner on the ther side contacts the ground, pivot point may go to the current corner making the box continue to rotate in anti-clockwise direction.(don't know if you can get it or not~~~sorry for that

)
for the solution, I suggest using keyframing since it is more flexible.
if u want to set key in rigid body, u can using active/passive key. make sure u know how it works in the doc.~~~good luck