Can you try the below, substituting your user name in place.
userdel YOUR_USER && useradd -g YOUR_GROUP -d YOUR_DIRECTORY YOUR_USER
In the above :
YOUR_USER : an ls -al against your web directory should look like this : YOUR_USER(owner) YOUR_GROUP(the group) PERMS (I typically think 755 for doc roots.).
It sounds like your permissions are wonked up. If for example, /var/www/site/bin had the wrong permissions OR any thing along the path, you would see issues like that.