They saw proof in person that was clearly convincing, and furthermore his personality fit with who they thought was satoshi.
This scenario is made impossible because of this Dave Kleiman guy and also the fact the Craig Wright is totally clueless about any technical issue related to bitcoin.
The closest possible person in here for Satoshi is Dave Kleiman, not Craig Wright.
If the person Gavin communicated with on 2009 and 2010 was really Craig Wright, how did not Gavin notice back then that he is communicating with someone that is totally clueless?
On the other hand If Gavin in 2009 and 2010 communicated with Dave Kleiman as Satoshi how did he get fooled in 2016 to think that the personality of Craig Wright matches with what he knew as Satoshi, ie Dave Kleiman?