Izaya doesn't even question it, moving to remove his own pack in order to locate some material with which to follow the other man's advice; he fully intends on keeping it close to his chest, not wanting to risk drawing too much attention to himself and being dragged off for 'rehabilitation', but he's disinclined to believe the story they've been fed so far. He doesn't doubt his 'dream' life existed, not even for a moment.

"Unreliable knowledge, perhaps, but it's better than no knowledge at all," and he begins to wrap his face and head just as the other man had before him.