"I have already made my decision...", which is not true at that point
It's true in temporal sense, just not true in the more general acausal sense, where even in Transparent Newcomb's Problem seeing the contents of the box doesn't mean that the contents of the box are already-acausally determined, since being determined in this case refers to the (logical knowledge about the) distribution of states of the box in the possible worlds, not to the (knowledge about the) state of the box in the world you're observing (you don't even properly know which world is that at that point, so can't use the observation to refine the model that describes the possible worlds under study, so long as you work with all of them, without updating away those inconsistent with observations).
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.