It's definitely a pretty weird and probably a bit scummy tactic by the game I'd say. The quest goes against your typical logical ways of avoiding death and forces you to play specifically by the "remove this buff or just get killed" rules.
The problem is also compounded by a distinction that isn't ever explained and kind of just exists. Some things are an attempt to inflict death with X% chance, like most instant-kill NPs, and some things just kill you, like Arash or Chen Gong's NPs, or Anra's timed self-death on his third skill. Chen Gong can even use his NP to sacrifice Gramps who has Death Immunity passive. Specific demon pillars can also absorb a servant which is also Just Death. The clock icon sounds like the same icon I see when the demon pillars do that. Up until you mentioned the clock icon I actually also thought the Hassans were regular death just with an insane rate, but apparently not?
Even if you know about that distinction the Hassan Parade is a bit of a little mess because you don't know what kind of death it's going to give you. And the player is never given any information that death can't be Debuff Immune'd, or that against all logic, death resistance doesn't help to cancel forced death. As far as I'm aware, the demon pillars and now the Hassan Parade are the only enemy-casted sources of forced death that I'm aware of. Anything else that comes to mind is normal and resistance plays into it as expected.
Anyway, just for reference that may help in a few days when it becomes available, the challenge quest that is actually against Gramps DOES work under ordinary death mechanics, he just has a strong rate of death, so BB is particularly very useful *there* for sure.