boguing,
"There can't be an angle (of attack) without a vertical component."
This is not true. Look at at a simple plane, flying at a mid speed and mid AOA, straight and level. There is no vertical component, but there is an AOA.
"If this weren't the case how would you explain the tip stall of an incipient spin?"
In this case there is a vertical component. But there doesn't have to be.