For the word учени́к, both accusative and genitive look the same: ученика́.
For animate masculine nouns, genitive and accusative looks the same.
It's actually accusative (and not genitive) because only accusative is used for living people, even in negative sentences.
Hey, I have been on a number of field trips as a parent and teacher with students, and teachers who lose site of students is not as rare as you might think! However, having sentences that do not make sense to you help you to think about the format and grammar of the sentences. I think they are kind of fun to think of instances where they might be used!
Ok, I think I have figured out why people are confused by negation. Firstly, the rule that they are trying to remember has absolutely nothing to do with this Duolingo sentence. This one concerns the accusative.
I believe that the abundant confusion concerns sentences with the meaning "I don't own". There's a good explanation for that here: http://russianlearn.com/grammar/category/genitive. Also look at point 3 regarding the partitive use of the genitive case :)