I actually disagree with this. While flaunting wealth might itself be off-putting, it does at least imply that the person is conscious of how much wealthier they are than others. But the criticism of Romney is just the opposite: that it shows him as "out of touch", i.e. unaware of the vast difference in wealth between him and the average voter. The fact that the bet offer is seen as an unconscious slip is in fact integral to why it is supposedly damaging: it revealed that he doesn't think of $10,000 as a lot of money. (Rather like how Marie Antoinette supposedly failed to realize that cake might be less accessible to her subjects than herself.)

Mind you, I think this criticism is entirely absurd and facepalm-inducing: apparently the ability to (deceptively) signal to the public that one is an "ordinary person" is a more important quality for a president than being the type of person who puts their money where their mouth is.