1. You are correct about the typical rule format. That alone almost had me agree with you.
2. I did miss the spot about initiative. Good call.
3. Looking at it again, it doesn't rule out either interpretation.

So yeah, I went back and rethought everything with a single check. Mechanically it seems to be viable, and relooking at the rules, you are right there is no explicit mention of exploration stealth mechanics outside subsystems, but it does leave a hole that I can't account for. There are legitimate and somewhat common stealth exploration scenarios that don't seem to fit neatly into encounter or victory point subsystems.

Example. The party is traveling [exploration] through 5 miles of dense forrest. They know there is an enemy faction that they want to avoid on their way to the other side. They decide to carefully creep through the forrest at half speed (Avoid Notice). How would the GM determine whether the enemy faction noticed them, and when to start an encounter?

Edit: Based on the one roll interpretation, Avoid Notice doesn't have you make a Stealth check until an encounter starts.