The number of people who do not know an odd number of people

You knew it was true because of your background; you understand the question in the context it is given. Thus while there is nothing conclusively guiding you to one interpretation or the other in the grammar and syntax itself, you intuit the probable meaning based on the grammatical and syntactical formulations common to the context of the question. Your past experience informs your decision.

Let us say that I (Andy) am in a room with Bob, Claire, Danielle and Em, and I only know Bob.

I know Bob. Bob, as one person, is an odd number of people. Hence it is perfectly defensible, when talking about the people in the room, to say "I know an odd number of people".

I do not Claire, Danielle, or Em. Claire, Danielle and Em are an odd number of people. Hence it is perfectly defensible, when talking about the people in the room, to say "I do not know an odd number of people".

Hence, both are equally valid, logically and grammatically.