Great find, Ignacio. You’re correct!
From the team (and definitely not me 
):
The formula in the paper is slightly wrong, and the right way to think about it is in terms of random variables – if X comes from Binomial(n1,p) and Y comes from Binomial(n2,p), and if X and Y are independent, then X+Y is distributed as Binomial(n1+n2, p). A subtle point that is that the output of sortition on different accounts must be uncorrelated (so that X andY are independent). In the paper accounts are referred to by VRF public keys, and the VRF ensures this property. In our system now (where two different accounts could register the same VRF key) the address gets hashed into the VRF output before binomial sampling, ensuring independence.