It's how visibly public this is compared to Asuma keeping it more discrete. Shame in private (even if it really isn't) is easier to bear.
I mean, it's a few articles of clothing. I wouldn't call myself an exhibitionist in any way at all, but I'd streak through downtown without hesitation for what is in all but technicality miraculous magic healing. And I'd make that choice in a second, flat, if we discount any incredulity of a wonder like that existing in the first place. And they're in a (self explanatorily) lethal death game?
This is quite literally of those retarded "would you take out the trash in exchange for one gorillion dollars?" bullshit trade memes and they are pretending like it's some high pressure deliberation.