For starters I recommend to look this:
http://surfcity.kund.dalnet.se/spain_morato.htm
There is at least one claim on Morato´s list that seems to be inaccurate and it is a Hawker Fury claimed on 20.9.1936. When it comes to others, I can not tell if they were right are wrong.
But even if he overclaimed 2:1, he would still be a top ace of SCW scoring more than any Legion Condor pilot.
I´m quite sure that Morato´s air victories have been studied as he was such a famous pilot and the top ace. I remember to have read that some Spanish aviation historians have checked Morato´s score and found that more than half of it has been accurate. But I can not remember the source.
Republican claims can be doubted also. I have compared some of the claims of well known Republican pilots with loss records of Legion Condor/Aviazione Legionaria and to my disappointment only little could be confirmed.