Well I totally agree with your points, if the other person is saying that simply becoming an apostate is synonymous with treason and enough to warrant the death penalty- under any circumstances, war or not.
However, the interpretation I have seen requires BOTH conditions:
death for an apostate is only prescribed IF it happens at a time of war AND the apostate turns to fight against the Islamic state. In this way, it is compared to the crime of treason in Western countries.
since actual fighting against the state is required by this interpretation, isn't it kind of, sort of okay to compare it to treason?
Then again there are a couple of problems that I see even with this liberal interpretation..
1) What exactly constitutes 'a time of war'? Wouldn't some Muslims be able to say that as long as the whole world is not subdued in an Islamic state the world is in a state of war? The division of the word into "house of peace" and "house of war", as well as the Quran's last commandments and narrations that have Mohammed saying he's been ordered to fight until every person has uttered "la ilaha ilallah", could support their stance.
2) Would the Islamic state wait for this person to actually fight them... or would they want to be proactive and kill the person because they think there's a *potential* that the apostate will fight the state? According to this guy's video Umar would interrogate the person, and based on the outcome of the interview he'd determine whether the apostate was a "danger" or not. This definitely takes away from the apperance of justice in this interpretation. No modern government would condemn someone to death because they *suspect* that the person will commit treason.