They do dispute his right to any counsel for it at all- they're wrong there IMO, unlike Hamdi there are issues and facts which can be presented here to contest his detention.
The hard decision, which these living constitution fantasists cowardly avoided, is just how to give Padilla that counsel.
That is what the judge, defense and government asked these clowns to decide and instead they overturned Quirin for their own political reasons.
Fantasist activists.