Ssh – Via ssh, git-checkout into directory the user doesn’t own: “Permission denied”

The first thing to do in this situation is to use the -v option to ssh, so you can see what types of authentication is tried and what the result is. Does that help enlighten the situation?

In your update to your question, you mention "on another local Ubuntu". Have you copied over the ssh private key to the other machine?

The most secure way of doing it I would say is to have a group called git-readers

add git and www-data to it, then have the following folder structure:

/home/git - git:git-readers u=rwx,g=rx,o=
/home/git/repositories - git:git u=rwx,g=rwx,o=rx

This will allow www-data into the folder for reading, but only give the git user write access. Any other user can't do anything.

If you want to add additional writers, I would add another group git-writers and add the users and git to it as well as the git-readers group, then use the following structure:

/home/git - git:git-readers u=rwx,g=rx,o=
/home/git/repositories - git:git-writers u=rwx,g=rwxs,o=rx

Note the 's' in the group permissions. This makes the writer users use git-writers group as their default group. This will only work properly if the writers are all umask 0002.