Does that mean that if they have information which is "not favorable to the defendant" that they wouldn't have to disclose it?
No, but as a practical matter most unfavorable information is disclosed because it is contained either in statements made by the defendant, results of scientific tests (DNA, ballistics, etc.), and documents or objects which may have to be disclosed. They only have to disclose the items, they don't have to explain how they might be used against the defendant.
Under the federal rules, statements made by witnesses don't have to be disclosed until after they testify. However, I've seen federal courts order disclosure shortly before a witness testifies (24 hours) to avoid delays. I'm sure there's some variance there. The government sometimes keeps witness names close to the vest and doesn't disclose them until trial. This can lead to continuances which judges never like. So, the government has to take that into consideration.
BTW, a defense request for discovery, other than exculpatory evidence, triggers reciprocal discovery obligations.