Lic, the Turks were on vacation in Wutai by coincidence, that's the point. They have a standing order to find Corneo as part of their general 'hunt down fugitives' duties, but they're off the clock, and so don't care that Corneo is running free until one of their own is kidnapped.
You're not wrong that there is a degree of subjectivity, but I do feel that there's also an objective element in whether the character readily lends themselves to what the plot wants to do with them -- and also that this is a reasonable enough qualification to include in the rubric.
Everyone agrees that there are objective elements, but no one agrees on what the objective elements are. Huh.
Lucrecia fits perfectly into what the plot wants to do with her, she's exactly what the story needs in her role. The character is perfectly consistent, there's no actual storytelling problem in anything she does except that some people don't like some of it.
Genesis is also consistent, he has done everything he's done in search of a cure and revenge, so post healing he doesn't need them anymore. He's not, like, trustworthy or anything. We're not asked to believe he's redeemed, just that Zack doesn't want to kill him. The secret ending of Dirge seems more 'oh crap, what's he going to do next' than' 'happy reformed ending'. (An ultimania may say different). Even him being carried away to DG at the end of CC is more 'stinger sequel hook' than 'reformed epilogue'
I haven't played type 0, but none of AVALANCHE give themselves the benefit of the doubt. Cloud, Barret, Aeris, Tifa, Vincent, all of them default to blaming themselves when bad things happen to, near, or around them.
We have yet to see any penitence out of him for his numerous sins nor any noble action towards his fellow humans. Even the fact that he is supposed to now be devoted to the planet's protection may not mean diddly when his past behavior stemmed in part from zealous devotion to something non-human, and this new obsession could just be pretense for further megalomania.
Who else might that apply to, hmm?
There are times when 'invisible people offscreen are making them do it' makes sense. For instance, when Tseng corners AVALANCHE in the elevator in Shinra HQ. But if you use it too often, it starts to run thin.
The three remaining Turks were still loved ones to one another, and if they were still on the chopping block two months after "following through" (shhhh) on their end of the ultimatum to save themselves from execution, logically that potentially remains the case a few short days later.
Obviously things were different by the time of the Gongaga visit (unsure whether Scarlet even knows this), seeing as Rufus was in charge by this point -- but then why would the Turks be killing executives willy nilly anyway? Rufus probably isn't going to appreciate that.
Revenge? It's also entirely possible that Rufus would want Scarlet replaced, and give Tseng secret instructions to assassinate her or something. Scarlet cannot be banking on Tseng's super loyalty to Rufus which she's not supposed to know about. Or that Tseng might be holding enough of a grudge to not care what Rufus wants. If characters need to be metagaming to make the scene work, it's usually a problem. Scarlet has to be either thinking either 'Tseng is trustworthy' or 'I have him under control' but BC presents a masterclass in how goddamned difficult it is to make the Turks do anything they don't want to do. Shinra spends the entire game trying and failing.
We saw the Turks under threat in BC, and we saw mainstream Shinra's very limited ability to act on those threats. Only overwhelming force stood a chance, and even that got pretty dicey.