This error can happen when you are accessing the SSH URL (Read/Write) instead of Git Read-Only URL but you have no write access to that repo.
Sometimes you just want to clone your own repo, e.g. deploy to a server. In this case you actually only need READ-ONLY access. But since that's your own repo, GitHub may display SSH URL if that's your preference. In this situation, if your remote host's public key is not in your GitHub SSH Keys, your access will be denied, which is expected to happen.
An equivalent case is when you try cloning someone else's repo to which you have no write access with SSH URL.
In a word, if your intent is to clone-only a repo, use HTTPS URL (https://github.com/{user_name}/{project_name}.git) instead of SSH URL (git@github.com:{user_name}/{project_name}.git), which avoids (unnecessary) public key validation.
Update: GitHub is displaying HTTPS as the default protocol now and this move can probably reduce possible misuse of SSH URLs.
