Hey @PaulH ! And welcome to Community! Apologies it took us so long to respond here!
To access the application logs for a piece of content on Connect, a few things must be true:
- The content needs to have logs (i.e. logs will not be shown for static content types)
- Either the user is an administrator or they are a "collaborator" on the report's "access controls."
("collaborator" includes the owner) 
(NOTE: in order to be a collaborator, the user has to be a "Publisher" role. But being a publisher is not sufficient)
I hope that helps!