I could be wrong but " When Dark Depths has no ice counters on it, sacrifice it " isn't that a game state based check and thus cannot be responded to because it doesn't use the stack ?
It is a "state trigger" as opposed to a "state based action." State based actions are things like "a player that is at 0 life or less loses" or "a creature with 0 toughness dies" or the legend rule. A state trigger is a triggered ability that looks for a particular game state. State triggers can be responded to.
603.8. Some triggered abilities trigger when a game state (such as a player controlling no permanents of a particular card type) is true, rather than triggering when an event occurs. These abilities trigger as soon as the game state matches the condition. They’ll go onto the stack at the next available opportunity. These are called state triggers. (Note that state triggers aren’t the same as state-based actions.) A state-triggered ability doesn’t trigger again until the ability has resolved, has been countered, or has otherwise left the stack. Then, if the object with the ability is still in the same zone and the game state still matches its trigger condition, the ability will trigger again.
Example: A permanent’s ability reads, “Whenever you have no cards in hand, draw a card.” If its controller plays the last card from his or her hand, the ability will trigger once and won’t trigger again until it has resolved. If its controller casts a spell that reads “Discard your hand, then draw that many cards,” the ability will trigger during the spell’s resolution because the player’s hand was momentarily empty.