"He does not drink oil."
Translation:Han dricker inte olja.
Yes, I get the difference but would that actually change anything in meaning? Because in Dutch it wouldn't.
In very many contexts you could use either, but in some contexts the difference matters.
If you're asking why the other way around isn't an accepted answer, it's because this is a language course and since the difference is the same in both languages in this case, there's no reason to change construction when translating the sentence.
If you're trying to understand what the difference is, not and inte negate the verb, so you could be talking about what someone is doing at the moment (remember that dricker is both 'drinks' and 'is drinking') – 'What is he doing? Is he drinking oil?' in which case 'He drinks no oil' would be a somewhat funny answer.