Not quite. Breaker's effect is a mandatory effect that activates when it is summoned to the field. At that point, the turn player's priority of activating an effect has been used, and your opponent can chain say Trap Hole. Since this is occurring in a chain, it is also the reason why you can't use Breaker's token to destroy Trap Hole, because it hasn't resolved to be placed yet.
The Creator's effect is optional. Therefore, when you summon him, you have the opportunity at that point to activate his effect becore your opponent can Trap Hole him. The fact that The Creator's effect is not a cost only affects the instance where his effect is negated. If you activated Creator's effect and your opponent chained "Divine Wrath" you wouldn't have to discard a card from your hand.
An example of the opposite would be if you activated Magic Jammer. If you opponent chained 7 Tools of the Bandit to negate Magic Jammer, you still would have to discard because activation costs are paid at the point of activation, not during resolution.
If your opponent chained Bottomless Trap hole to the activation of the Creator's effect, it would look like this:
Chain 1: Creator's effect (Note: no card discarded at this time)
Chain 2: Bottomless Trap Hole
Now we resolve backwards...
Resolution 1: BTH destroys Creator and removes him from play.
Resolution 2: You discard one card from your hand and special summon a monster from the graveyard. The Creator's effect does not require him to stay on the field for his effect to resolve.
Hopefully this clarifies things a bit more.
EDIT: The DMoC combo with the Creator unfortunately won't work. The first thing you do is name a monster in your graveyard THEN you discard a card from your hand. Since DMoC isn't there yet (unless you have another in your graveyard) you can't designate him.