I agree with all of the bullets you posted and the line of thinking in general. But sometimes the undeserving DO get an award. What then? Years in consulting and management taught me that there are two cases: 
 
1) The person thinks they are deserving. In this case, others in the organization are correct in their assessment that the system is flawed. Often you will hear such organizations referred to as "political" and the winner as someone who "manages up." Morale certainly will drop. If the reward is part of a pattern, people will certainly leave, knowing that factors other than competence and hard work are what is important in the organization. Those that remain will spend ever more time on playing politics instead of doing their jobs. If you incentivize bad behavior, you're left only with those who behave badly. 
 
2) The person knows they are unworthy. This is a lot more complex situation. The person can then accept, defer, or decline the reward. In the first case, the person must find a means to follow through on the intent of the prize. For instance, one can argue whether the President's "donate it to [an unspecified] charity" was sufficient here or not. In the last case -- declining the award -- there is a strong risk of embarrassment for those who made the award. You will almost certainly burn a bridge, denigrate the awards process, or both.  
 
But the "defer" case is the most overlooked. What if the President had asked the committee to hold the award in escrow, based on the achievement of goals he set for himself? As one of your contrary responses indicated, perhaps the prize was given as encouragement. (That's what the Nobel Committee claims.) If that's the case, deferring not only bolsters the award process, but also the honoree's credibility. A little delayed gratification... and hard work to become worthy of the award in the interim... is the best outcome of an otherwise awkward situation.