Does Ward trigger if the spell targeting the creature was cast by its own controller?

Ward is a triggered ability that reads, in essence: "Whenever this permanent becomes the target of a spell or ability an opponent controls..." — wait, that is actually the key point. Let's check the actual rule.

Per CR 702.20, Ward triggers "whenever [this permanent] becomes the target of a spell or ability an opponent controls." The word opponent is crucial: Ward only triggers when a spell or ability controlled by an opponent of the Ward creature's controller targets it. If the creature's own controller casts the spell, Ward does not trigger.

So the correct verdict is: No, Ward does not trigger if the spell targeting the creature was cast by that creature's own controller. The controller can freely target their own Ward creature with spells and abilities without paying the Ward cost or having the spell countered.

Example: You control a Raffine, Scheming Seer (which has Ward 3). You cast Slip Out the Back targeting Raffine to protect it. Because you control both the spell and the creature, Ward does not trigger, and you pay no additional cost.

This is a common misconception. Ward is a defensive ability against opponents, not a universal tax on all spells. Only spells and abilities controlled by an opponent of the Ward permanent's controller will trigger it (CR 702.20b).