Due diligence is an important aspect of buying a domain name. Whether a buyer is acquiring a domain name privately without the assistance of a third party, using a domain broker, buying a domain name via auction, or using an aftermarket platform, due diligence is critical to ensure the domain name acquisition is legitimate.
I don’t think auction platforms do much (or enough) due diligence on domain names that are listed for sale. I believe some confirm that the customer who listed the domain name is the registrant of said domain name, but I am not even sure if that happens for every domain name nor do I know if it happens with every venue. Even if this is true, a thief who stole a domain name and has possession of it could easily prove possession of the domain name, so this is not much help.
As part of doing due diligence, it can be helpful to contact previous domain registrants to track the history of the domain name. DomainTools’ Whois history tool is the primary tool I use to see the historical Whois records for domain names. I believe DomainIQ also has some historical Whois records as well. Google searching for Whois and the domain name may also reveal some (spotty) results.