p.4: “in reality the distribution of spin for each component in the binary may differ systematically due to different formation and accretion history, but our analysis is not sensitive to the magnitude distribution at this level; see below”. First, drop “and accretion” — we state elsewhere that we don’t expect accretion to change the BH spins in high-mass XRBs, and the same applies here. Secondly, the magnitude distribution isn’t really the issue (as we point out, we are more sensitive to the projections); the problem is that the angular distribution could be very different for the two components depending on formation history. So my proposal is just to say "in reality the distribution of spins for the two components in the binary may differ systematically due to the formation history”.
Comment from Ilya: