Is there a way to compare local clone of a GitHub repository to a repository in GitHub which is effectively the master repository to confirm that the local clone is a sub of the GitHub repository?
Because of the nature of git (last commit implies the entire history of that branch), you can validate it by comparing SHA1 of last commit to a credible repository's one.
A simple shell code snippet can be like this (assuming you are only interested in master branch):
if [ $(git rev-parse master^{commit}) == "<official sha1>" ]; then
echo "Good"
else
echo "Bad"
fi