The big picture answer is because our military is established with civilian control and thus we render honors to leadership of the civilian government.

The detailed answer is there is a long list of elected civilian leadership who are due honors from the military. The secretary of defense, secretaries of the branches, president of the senate, speaker of the house, chairs of committee's, etc. The list is long and would take a PAO and probably the AR to reference them all in the correct order.

Definitely a case of salute the rank, not the person

Ok, Dick Winters

There's no requirement to salute the VP. There is also no requirement for either the VP or President to return a salute. My guess is the commander of the honors detachment, at some level, decided saluting her was easier than having to explain why they didn't...time after time after...

Army: AR 600-25

Short answer: she should be rendered honors and saluted when visiting a military installation

Long answer: who knows what orders or policy the honor guards follows. CO's are obsessed with adding to.. because they can't take away. /Bitter Former NCO

Just like flags going half-mast: when you let politicians control military ceremonies, they will abuse them to stroke their egos and those of their friends.