Yesterday I tried to running shot on an object that KG Beast was standing on. I was told KG Beast because he doesn't have stealth blocks LOF to the object and therefore I couldn't destory it. I've never heard that characters block LOF to objects they are on. Would I have been able to destory the object or no?

You should have been able to destroy the object.

Characters do not block line of fire to the square they are in.

This becomes important for Telekinesis attacks.

Stealth says LoF drawn to the character that pass through hindering are blocked. The operative word being 'character.' You should have been able to.

What these guys said.

Can someone word me the rulebook please?

Word

STEALTH When it is not your turn, hindered lines of fire drawn to this character are blocked.

DESTROYING OBJECTS Objects can be destroyed using the rules for destroying a square of blocking terrain (see p. 13).

DESTROYING BLOCKING TERRAIN A square of blocking terrain can be destroyed by a single attack that deals at least 3 damage. When a character attacks blocking terrain, the attack automatically succeeds. A close combat attack can be used to destroy a square of blocking terrain adjacent to the attacker. A ranged combat attack can be used to destroy a square of blocking terrain by drawing a line of fire to the center of the square of blocking terrain; the line of fire is not blocked by the target square in this instance.

Every Charater has an Inviso Ray! I wish objects made hindering terrain when destroyed.

A long time ago Objects use to become hindering terrain when destroyed. But the rules where changed a long while back so that did not happen and to help rein in stealth a little.