The House example you gave I actually liked very much, didn't really think of it before but it applies rather well to the whole detective situation (but then again that's the point of the show). Nonetheless, you must also remember that in the show, as in real life, they make multitude of exams that reveal plethora of things and, most importantly, have the person in question at their disposal for any kind of tests or questions they need to make; the detectives here count with nothing but lying people and second-hand info. The pregnant example sounds like a bit of a stretch, but then again House once had a patient who complained that everywhere he touched it hurt him (spoiler, his finger was broken); doctors typically go from obvious to rare, but then again this is not about doctor work but detective one, in which the same statement applies just as true.
Sure, not knowing some things are outright sins, but then again, it's only human to sin (mwahahaha). Taking once again an example from House, doctor Foreman once had a cocky episode and ended up literally killing a patient due to his hubris, this worked to humble him a ton and made him ever more meticulous and careful with his diagnostics. People often make mistakes that can end up with dire consequences, both for him and the people involved, and that's what makes them all the more human and less Sue-ish.
Now then, back to the detective. We must take into account that the detective made this case personal and models it around his own circumstances, so his judgement is clearly clouded. It's very possible that he has the possibility of her running away in a corner of his mind, but he doesn't pay much attention to it because of both panic (this is a serious case and he has to hurry) and all the evidence so far (bad testimony and bad people) points to something else, that or his own past is telling him what he would do in her situation. You don't see a guy clutching his leg in pain and instantly assume that it's his hands that's in pain and he uses his leg to stop the blood flow, you go instantly to the obvious and then work from there to the less obvious and the outlandish. He only knows now that there WAS a kidnapper, since there was no previous indication about her being close to any male of any age beyond his father, hence his reluctance to believing she ran away with someone; it couldn't have been by her own either since she pretty much had no one else to rely on.
There's also into account something that most people fail to take into account whenever they read manga or watch anime, which is: they are in Japan, with Japanese culture that's different from our western culture. Sure enough, this doesn't excuse everything, but after reading a few (hundred) manga and watching some videos about it, you start to get why some people tend to avoid making a scandal or allowing people to step over them... sometimes...
Also, sure enough, he knows that the parents lied about Sachi being abused and the time of her disappearance, but that's as far as the knowledge they have goes, they have no clue on the extent of the abuse, the reasons for it nor do they know about the exact time and circumstances of her actions; he even said that it was a worse case scenario and that he didn't know the full extent of what happened and he's deducing based on circumstantial evidence and personal experience.
People more often than not tend to assume malice unless there's proof of the contrary, which only worsens when there's personal feelings involved in the matter, he is simply assuming the worst and acting accordingly, since it's much easier to apologize to an angry person than to apologize to a corpse. Sure enough, being genius means being able to think outside the box and reach an answer by looking at it from outside, but that only works for certain situations and doesn't really apply all of the time, they are still human and still make mistakes, making assumptions and letting past experiences dictate their actions, because for as genius as they may be, they are still human. Not to mention that, so far, the only person to ever call him a genius is himself, who comes from a no-name detective agency; his statement may as well be as flawed as the testimony he gets.
And about my high note... well, that was my bad, I originally meant end-note but wrote the wrong thing and only realized afterwards. Anyways, sure enough, in scanlating business many things get lost in translation, but at the end the meaning prevails (in the good groups at least): he wants to save xxx, mostly as a way to "save his past self", but save her nonetheless.
Well, at the end of the day, what you said did make me change my mind about some things. Can the detective guy be considered a genius? Hardly. Did the mangaka do a good job portraying him? Doubtfully. Are his thought processes well defined and properly thought out? No way Jose. Does all of this make this a bad manga? ABSOLUTELY NOT. This hasn't exactly been a masterpiece, but then again this was originally a side-project that the mangaka make in his pixiv and that got serialized due to the high response, with none of his previous works being what you would call a literary masterpiece either or a perfectly written one, so I say we give him a bit of a leeway in this.
Besides, we're here for the mush and the good feelings, not to watch Hawaii Five-O or Sherlock.
