It sounds to me like he is describing his distribution over probabilities, and estimates at least 50% of the mass of his distribution is between 1/1,000 and 1/1,000,000. Is that a convenient way to store or deal with probabilities? Not really, no, but I can see why someone would pick it.
The problem with this interpretation is that it renders the initial statement pretty meaningless. Assuming he's decided to give us a centered 50% confidence interval, which is the only one that really makes sense, that means that 25% of his probability distribution over probabilities is more likely than 1/1000, and this part of the probability mass is going to dominate the rest.
For example, if you think there's a 25% chance that the "actual probability" (whatever that means) is 0.01, then your best estimate of the "actual probability" ...
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