Should this translate to "I think not" with "I don't think so" as an accepted alternate? As in, should it suggest "I think not" when you respond with "I don't think so?" And then leave "I don't think so" for "Я так не думаю"? This sentence (Я думаю нет) seems more certain, which matches up with the certainty of "I think not!" in my opinion. The only experience I have with Russian is via duolingo, though, so please correct me if I'm wrong.
This interests me as well. I sort of get the impression (again) that the sentence could mean a lot of things, depending on the intonation and what else that is not expressed here. It feels like it could be maybe a bit forward and authoritative, like "I'm telling you... no. (you're wrong)", indeed like "I think not!". Or it could just mean "I disagree". I don't know.
On a sidenote, has anyone noticed there seems to be quite a bit less discussion once you reach a certain point on the course (right around passing the first checkpoint)? The content is getting ever so slightly more advanced, but you're actually relying more on your own random guesswork. (don't know if this is really true either, just an observation. average 5 comments instead of 50 in the basic tasks)