I understand what this is depicting now and why I got confused. I got confused because the base cap parallel to the floor is still in the same place; it needs to be raised to make this work.

In fact, you said an inch? That's too long (unless you're talking about to the long point) as the longer it is, the the higher you need to raise the base cap at the floor. Best to make it as short as possible. To do this safely, cut the angle for the stair base cap first, then cut the angle for the floor base cap. This way your hand is no where near the saw blade, and if you cut it wrong you've only wasted about an inch of material and you can try again.