Seems fully legit. «Put another way» completes what the original poster wrote, in a different telling perspective.
The OP said, "A will refrain from B under condition C: the general intention of A is to refrain from B".
The replying poster noted, "Admitting that A intends to refrain from B under condition C, the intention is also not to refrain from B, failing condition C".
The replying poster is correctly noting that the relation is not just "C→¬B", but "C→¬B ∧ ¬C→B".
FooBarWidget notes one half of the story; throw10920 remarks that the other half is also present. Correctly one states - reassuringly - "do not see a false extreme: B is not an absolute set intention", but the other notes that at the same time it should not be forgotten that "B is a set conditional intention". Which is what A has stated for a long time: "the reunification will happen: peacefully if possible, coercively otherwise".
The 'put another way' formula is logically imperfect but rhetorically admissible, it is in a clear context. Of course throw10920 did not "repeat" what FooBarWidget wrote, «what was said»: he proceeded in the debate from the immediately preceding move posing a new "line".
It is a "put another way" not in terms of restricting to the original poster's idea (thus re-reading it), but starting from the poster's idea in the context of given information.