> But can I add this information just because I think that this is the question? I mean, this example is obvious, but there could be questions where I add false informations I think are correct.

Well, instead of editing the question to add missing information, you rather should leave a comment for the OP to clarify and improve their question (as you did already).

As you mentioned such edits may quickly become speculative and obfuscate the real problem stated in the question.