The rules reference says;

MOVING THROUGH

When executing a maneuver, a ship moves through an obstacle or another ship if its maneuver template overlaps that obstacle token or that ship’s base. A ship can move through another ship without issue, but moving through an obstacles produces the effects described in the “Obstacles” section.

Obstacles acts as hazards that can disrupt and damage ships. When a ship executes a maneuver, if its base or maneuver template overlaps an obstacle token, it executes its maneuver as normal but suffers an effect based on the type of obstacle:
A ship can still perform free actions even if it moved through or overlapped an obstacle, as long as the ship is not stressed.

Stunned Pilot and the FA * for Stunned Pilot says;

Stunned Pilot
After you execute a maneuver that causes you to overlap either another ship or an obstacle token, suffer 1 damage.

FAQ p.9
If a ship with Stunned Pilot assigned to it executes a maneuver in which the maneuver template overlaps a ship or obstacle token, but the ship’s final position does not overlap a ship or obstacle token, the effect of Stunned Pilot does not resolve.

Finally Advanced Slam the FAQ talks about Advanced Slam ;

After performing a SLAM action, if you did not overlap an obstacle or another ship, you may perform a free action on your action bar.

Overlapping an obstacle occurs when the maneuver template or the ship's final position overlaps an obstacle. Overlapping a ship occurs when the ship's final position would overlap a ship.

Given all the the entries above I believe the FAQ contradicts itself when it comes to Stunned Pilot and Advanced Slam. If you use the Adv Slam ruling (because it's the newer ruling) then Stunned Pilot * should * then cause extra damage, right? It seems that Moving Through an obstacle is an overlap because it's overlapping per Adv Slam entry.

With the clarifications above you could effectively read;

After you execute a maneuver that cause you to overlap another ship (Overlapping a ship occurs when the ship's final position would overlap a ship) or obstacle token (Overlapping an obstacle occurs when the maneuver template or the ship's final position overlaps an obstacle. ), suffer 1 damage.

This is important because cards like x7 title and Flight Assist Astromech allow a free action after performing a maneuver if your didn't overlap a ship or rock. If you didn't see the adv slam ruling and only the Stunned Pilot and Rules Reference it would seem those two upgrades would work if you cleared the rock (via Moving Through) and didn't physically overlap another ship or obstacle.

Quote

If you use the Adv Slam ruling (because it's the newer ruling) then Stunned Pilot * should * then cause extra damage, right? It seems that Moving Through an obstacle is an overlap because it's overlapping per Adv Slam entry.

No, because the Stunned Pilot ruling is specific to Stunned Pilot.

The way I see it, Stunned Pilot assigns a damage if and only if the ship's final position overlaps, a situation which is unique to Stunned Pilot, hence a specific FAQ entry. A ship with a Stunned Pilot still suffers the normal effects of the maneuver template overlapping an obstacle, but this by itself will not trigger the extra damage from Stunned Pilot.

It's a case of FFG using the FAQ to make a 'just cuz' ruling that reduces the power of certain upgrades (ASLAM & /x7) without making an official errata.

Similarthing to Genius+Trajectory; as written it works because the reference uses an 'instead' clause, but the FAQ "clarification" says it doesn't. Contradictions between similar situations in the FAQ are becoming more common where errata could have been used to change the words to work as intended.

What happened with Advamced SLAM was the card was clearly intended to work with the same rules as a standard maneuver for whether or not you get the action. So flying through a rock should block using it. Unfortunately for the reasons you have pointed out the RAW would seem to indicate that that's not what would happen. So rather than errata the card to just say "If you pass through or overlap an obstacle, or overlap a ship" they just put a "clarification" in that contradicts other rules.

Unfortunately these sorts of things are getting more numerous as the game ages, which to be fair is a bit inevitable to a certain point with imperfect humans managing it but it is still annoying.

I'm getting more in favor of a 2.0 as time goes by but at the same time not looking forward to my large and expensive collection being invalidated.

Luckily Stunned Pilot was updated so that FAQ clarification is only needed with the old damage deck. The new Stunned Pilot reads:

"After you execute a maneuver, if you are touching another ship or overlapping an obstacle token, suffer 1 damage. "

They could probably errata the original Stunned Pilot to use the same language as the new one, but I don't think FFG is interested in modifying any of the cards in the original damage deck.