I'd be really interested in an example of where this is the case. Personally, I can't conceive of a situation where, in a perfectly fair system, the man with the most money is utterly intolerable. Such a system naturally creates the inference that the man did something as an individual to acquire that wealth (and not necessarily in a zero sum manner).
As pointed out in the article, the issue with rising inequality is not that the wealthy are getting wealthier necessarily, only that it comes at the expense of people who work just as hard or harder, but still struggle to get by from day to day. Since the perception is that more work leads to more reward in a fair system, the perception is also that this situation is unfair.
Economic equality, however, is not necessary for such a situation to be fair. Flipped around, if the manual labourer who toils hard every day were paid more than the non-executive board member the situation would be perceived as fair, despite the fact that the two individuals would receive different compensation.
I really can't see the difference between "fair" and "unequal" being a matter of "semantic quibbling".