When you connect your Github account to Docker Hub, that will give DH full access to all repos (https://i.imgur.com/4jJWrez.png). I'm not even sure if Github's permission model supports adding only read access to private repositories.
I'm not 100% sure if Docker hub uses deploy keys for repos it has access to thru the integration, but at least previously there was an option to manually add one to repository if it couldn't access it otherwise.