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I mean it makes since people don't just stab the thing in it's eye but still surprising! Link to the relavent factoid?
A few examples I found from Batman Beyond.
View: https://youtu.be/pYMui8JWkr8
View: https://youtu.be/KQwfFqZcyPc
and some backstory from various comics, and the animated series.
View: https://youtu.be/GRUHvUlnKZU
View: https://youtu.be/H2lIoCMuo24
They take control of their hosts powers when they attach themselves to one, it's why a New God like Birta couldn't just overpower the one on her with Superstrength at first. Kai-ro's shield was off when it latched onto him so nothing of note there. Warhawk didn't have the strength to tear through the one on him with just his talons, something he has done to Apocolypse Warbots easily. Later on, in the fight against the possessed JLA members, Terry shocks a whole swarm with his suit, and yet when he does this to Aquagirl she just shrugs it off, Atlanteans' are resistant to the shocks of electric eels, a little-known fact from the old comics that shows how it protected the Starro in this instance, only when that boulder knocked her out did they get it off with Supermans help.
I was wrong about Martian Manhunter, I knew about the comic where he fought Starro alone and was taken but I was unaware about how he did it to himself, and who would expect a god damn coloring book to be the only example showing that his phasing worked to get them off?
As for my Superman example, in Batman Beyond when Superman chases Batman he busts through ice without anything to protect it from debris and was affected by the Kryptonite just like Clark was, so weakening Clarks powers weakened the Starro as well. I couldn't find video of the fight before where he was knocked out, so I suggest finding the episode for yourself if you want a look, it's Season Three, Episode Two, The Call part Two.
Though most of this can be taken as conjecture, showing is better than telling, so seeing these heroes subdued by just being in contact with these creatures is enough proof for me that they take on aspects of their hosts powers to protect themselves while connected, but only those aspects that prevent the host from hurting themselves with their powers though, they can't suddenly sprout laser eyes from being on Clark or create Lantern Constructs without a ring.