One thing worth checking is whether an older cached wheel or .egg-info is interfering with the installation.
Even if you request 1.2.2, pip might still be picking up 1.2.3 from a cache or a dependency resolution quirk.
Try running the command with --no-cache-dir and force reinstall:
pip install --no-cache-dir --force-reinstall MySQL_python==1.2.2
Also, verify if any requirements.txt or other scripts are getting triggered after install that might be overriding your version. That tripped me up once in a clean venv too.