Help regarding cross-matching catalogs! Separation and match_catalog_sky

I am trying to crossmatch the latest Fermi LAT catalog to an sdss catalog. I found tsuji et al. 2021 where they create a distance profile and use it to decide the cutoff. I did it by using a separation function in astropy but the histogram shows a linear increase where I was expecting a bump near 0 and then a linear increase.

Then I used the match_to_catalog_sky function and in the output there is the bump but not the linear increase… WHY!!!

I created a random catalog to check number of false matches and whether the distribution was a result random matches. I did a KS test and I got KS Statistic: 0.7842946490618485, p-value: 0.0 . Is it correct to just use the output from the match_to_catalog_sky function and setting the cutoff from CDF of the d2d of random position catalog? What is the significance of the distribution close to 0 and no linear increase?
Thank you!