Translation:They only study an hour a week.
Actually 'only' can come before or after the verb, but with a slightly different sense: 'they only study ...' suggests that they should study more, whereas 'they study only ...' is merely informative.
I like that you look for fine distinctions in use of words, however I think that you are putting too fine a point on the use of the position of 'only' in this case. I feel that the use of 'only' in the sentence, whether before or after 'study' suggests that they might study more ... omitting the 'only' provides mere information.
I think people read too much into this. Its simple, they only study an hour a week means they only study an hour a week. You would have to know the context of the conversation not just the sentence. Some folk will read it as they should study more, some will read it as they are lucky only having to study an hour a week. Horses for courses.