A WebmasterWorld thread claims that Google has told him that they are not able to manually remove a minimum bid requirement in AdWords.
His AdWords representative told him that "it was a common misconception that they are able to remove the $10 minimum bids manually and they told me that the "penalty" is never applied manually."
From all that I know about the quality score algorithm, is that the algorithm is fully automated. I have never seen a thread stating that Google can manually remove that minimum bid requirement.
But I have seen Google recommend that you can restart your campaign to start from scratch and try to improve from there.
There is obviously a debate about this taking place at WebmasterWorld.
One member is convinced their is a manual component to the AdWords minimum bid requirement:
There is definitely a Manual component to the penalty. One of my sites was hit in last QS update. It has been a long time since I changed the whole look and feel, added clear navigation..lots of additional content, reduced ads to one block per page (after the articles). No change in QS. The bot seems to be dead.
Forum discussion at WebmasterWorld.