In both cases, while computing them you never assume anything which you know to be false
Counterfactual mugging and the ransom problem I mentioned in the great-grandparent are both cases where TDT requires you to consider consequences of counterfactuals you know didn't happen. Omega's coin didn't come up heads, and your friend has been kidnapped. Nevertheless you need to consider the consequences of your policy in those counterfactual situations.
I think counterfactual mugging was originally brought up in the context of problems which TDT doesn't solve, that is it gives the obvious but non-optimal answer. The reason is that regardless of my counterfactual decision Omega still flips the same outcome and still doesn't pay.
Y'all know the rules: