I saw this too, I think he means 'maximum entropy over the outcomes (ball draws)' rather than 'maximum entropy over the parameters in your model'. The intuition is that if you posit no structure to your observations, making an observation doesn't tell you anything about your future observations. Though, that interpretation doesn't quite fit since he specified he knew they were drawn with a known probability.
One of the things EY made me realize is that any modeling is part of the prior. Specifically a model is a prior about how observations are related. For example, part of your model might be 'balls are independently with a constant but unknown probability'. If you had a maximum entropy prior over the draws, you would say something more like 'ball draws are completely unrelated and determined by completely separate processes'.
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I click on the link, and I can't scroll down past the bullet point about American Idol conversations.
It's just an image, not a real site. The link to the full article is in Bongo's comment.