As I see it, it is mainly linked to the speech politeness that is used. In informal speech, the question form is achieved by intonation mainly (and often, some additional particles at the end), so in writing the question mark is necessary. In formal speech, question particle is mandatory, so question mark is redundant (and thus, not used):
ex. informal: 食べる。"Taberu." (I) will eat.
食べる？ "Taberu?" Will you eat? (the subject is often ambiguous in Japanese, because it is not mandatory to include it)
or "Taberu no?" Will you eat?"
versus formal: 食べます。"Tabemasu." I will eat.
食べますか。"Tabemasuka." Will you eat? The "ka" particle indicates, that is is a question - the question mark is unnecessary here.
Or maybe you have some real-world examples, that one about you wrote? If so, please post it, and I will try to better grasp the case and explain it further.