Well, perhaps that's not so very mysterious. An expression of humility might just bespeak the person's desire to be seen as modest. Perhaps they feel they didn't really deserve the award - like when I won the fancy dress competition at my primary school and cried, because I thought it wasn't actually the best costume. I wonder how often that happens to grown-ups?
Conversely, people often say "I'm proud to be X", where X is a nationality or some other thing for which they can claim no credit at all, being merely a card dealt them in the lottery of life. While they might reasonably feel pleased or lucky to be born in X, or to have famous ancestor Y, where do they get off feeling "proud" of it? No one says, "I feel proud to have won the lottery": if they did, they would be laughed at. What's the difference?
I suppose it's that people's sense of self is partly social, and that you can feel pride in achievements of the wider group of which you are a part, even though you personally may have contributed nothing towards them - an attitude memorably mocked in this sketch. Similarly, you may feel shame in the actions of your wider group should you disapprove of them, despite personally having taken no part in them and even fought to prevent them. Hence the sight of Americans apologising on social media for the election of a man they never voted for.
On the one hand, the communitarian bonds this speaks of are admirable - but this way of thinking can obviously lead to injustice and prejudice of the "tarring with the same brush" variety.
It also explains the ease with which politicians and commentators are able to amalgamate populations with a wide variety of views and speak without qualification as if they were all of one mind. Thus Theresa May is able to talk about leaving the EU as "the will of the British people" and Nicola Sturgeon is able to say that "Scotland voted to remain", as if the millions who voted the other way were of no account - or rather, did not even exist. The fiction that "the British people" or "Scotland" are entities capable of will and decision-making, rather than groups of individuals whose individual decisions are triaged by an electoral formula, clearly has a powerful political function. You will never hear May say, for example, "Most British people voted to leave", let alone "Most British people who voted, voted to leave", still less "Most British people who had a vote and who also voted, voted to leave" - any of which would represent the case more accurately. The fiction of "the people" and its "will" legitimates the extremity of their actions. But without it, perhaps there would be no action at all?