I think he's classy because he has so many ingrained behaviours and never behaves inappropriately, never talks about money, is kind without any kind of expectation, never shows off and never lets himself down.
But surely many of those 'ingrained behaviours' in themselves don't necessarily have any positive value except as social class markers? I mean, there's nothing inherently wrong with, say, eating in the street or talking about money, any more than there is with saying 'pardon?' rather than 'what?' or lounge rather than sitting room?
And it's easy not to be a 'show off' if you're secure in your privileged place in the world, or to discuss money if you've always had it, whereas someone who has had to struggle for everything they have could be pardoned for drawing attention to it in case it's taken away again, or being preoccupied with earnings and the cost of things.
Obviously, it's probably generally more pleasant to be around the former than the latter, because they're not implicitly demanding any form of acknowledgement from you, but that's only because circumstances mean they don't need it.
What do you mean by 'never lets himself down'?