This was work by Max, and I never got too into the particular algorithm details.
That said, I believe it was something about “getting enough randomness” for a uniform distribution over a given range. If you have 32-bits to produce 32-bits, it seems like you’d have to go in a predetermined order if you want to traverse every value, which is not very random at all! (E.g. every time you see 5 you know 8127 is next, then 902, etc. All the way back to 5.) Using 64-bits to produce 32-bits at least gives you 4 billion predetermined paths, so it would be harder to guess what comes after 5.
But again, I never got into pseudo-randomness algorithms, so this is just my basic intuition.