Why the Survey Corps doesn't find a human body inside each titan?
No. This is not a logical flaw in the series. Unfortunately, that information was only touched on in the last episode of Season 2. You've stated you don't want to hear spoilers about the manga. The anime ended right when the humans suspect regular titans are humans too. The last episode of Season 2 of the anime actually cuts out part of the conversation between Pixis, Hange, Levi, and Erwin where they address this. I assume either they will pick up in season 3 at that same discussion or use a flashback at some point to reveal the rest of what was said there. There's really nothing more I can say without spoilers, because I don't think the anime has given enough information to deduce what's going on at this point.