I played at a tournament and 3 different times 3 different opponents beached themselves on an asteroid like so:

They all claimed they got an extra defense dice for the asteroid. I told them no asteroid is blocking my shot, so they do not get the extra dice.

The TO could not find anything to support the "rule" that you get +1 dice when you're beached on an asteroid, so long as there is no bit of asteroid peeking through between his ship and my ship.

Am I correct?

If the asteroid you're on has a bit between you and the guy shooting at you, you get the +1 agility.

You DON'T get the +1 agility simply for being on a rock.

You are correct. Your opponents were wrong.

Ditto dracon. There has to actually be some asteroid between the two of you to get the +1 defense die.

The TO could not find anything to support the "rule" that you get +1 dice when you're beached on an asteroid, so long as there is no bit of asteroid peeking through between his ship and my ship.

That's because there is no such rule - "beached" is not an official game term.

Ditto Forgottelore's ditto of Dracon. Double ditto, I guess.

And here is the rule which supports your argument:

When measuring range during combat, if the edge of the range ruler between the closest points of the two ships overlaps an obstacle token, the attack is considered obstructed. Because of this obstruction, the defender rolls one additional defense
die during the “Roll Defense Dice” step of this attack.

Just to clarify things, you don't get +1 agility from the asteroid...

You get an additional Defense DIE. The distinction is important, because, for example, Wedge is never able to remove the obstruction die from being behind an asteroid, even if you have agility 0. Likewise, ships don't double the obstruction bonus die when targeted by single turbolaser turrets.

Just to clarify things, you don't get +1 agility from the asteroid...

You get an additional Defense DIE. The distinction is important, because, for example, Wedge is never able to remove the obstruction die from being behind an asteroid, even if you have agility 0. Likewise, ships don't double the obstruction bonus die when targeted by single turbolaser turrets.

Should be clarified a little bit more although it's already been stated.

The bonus only applies if there is asteroid between the shooter and the target. Some could read that and still think they'd get the bonus defense for just being on an asteroid.