Yeah, that explanation of priority raises more questions than it provides answers.
Then again, I'm only familiar with priority in traditional 2-D fighters, where any attack consists of an active (or red) hitbox overlapping a vulnerable (or blue) hitbox; when two attacks meet, the red hitboxes will pass through each other, continuing until one move meets and overlaps with the vulnerable hitbox of his opponent's move. So generally, whoever got the attack out first will win, because his move has a "headstart," but a high priority move can make up for the late start.
For Ground to Air in Melee, not all moves trade. Sheik can beat all of Falcon's aerials cleanly with her f-tilt. Bowser's Down + B will always lose to Fox's u-tilt. Maybe I'm using extreme examples, but there has to be others.
Edit: Why is there a random sad smiley below my avatar?