That's not how they caught him. They caught him because he posted a StackOverflow question under his real name that contained a snippet of the code that was found in SilkRoad's source code.
> The server running Silk Road was imaged and forensically examined in late July. This was done surreptitiously by the hosting provider at the request of the FBI via local authorities and the Mutual Legal Assistance Treaty. They used the server’s ssh config to find the VPN server Ulbricht was logging in from and the VPN server’s last login record of IP addresses to locate a cafe near his home. The FBI was able to correlate the location based on Google’s records of the email account that was previously used to solicit users and help on the Bitcoin Talk forums, which he accessed from home the same day he logged into the VPN server.
> The server running Silk Road was imaged and forensically examined in late July. This was done surreptitiously by the hosting provider at the request of the FBI via local authorities and the Mutual Legal Assistance Treaty. They used the server’s ssh config to find the VPN server Ulbricht was logging in from and the VPN server’s last login record of IP addresses to locate a cafe near his home. The FBI was able to correlate the location based on Google’s records of the email account that was previously used to solicit users and help on the Bitcoin Talk forums, which he accessed from home the same day he logged into the VPN server.
https://www.comparitech.com/blog/vpn-privacy/staying-anonymo...