To be fair, it's perfectly understandable that Jeremy passed the tests. Jeremy is an alcoholic who was sober. When he entered the house the first thing he did was start drinking - from all the time we saw him on our screens, he wasn't sober! Not once. After nominations he admitted to have over 10 glasses of champagne.
The real question is why C5 didn't intervene when an alcoholic began drinking. Surely they have a duty of care to the housemates?