Since the news came out that income mobility in this country, while crappy, has actually been pretty bad for a while, there's been some changing to the inequality debate. Mostly not in a good direction. It shouldn't need to be pointed out that mobility and inequality are very different issues. It is possible to have very high mobility with simply insane inequality. Imagine a country where the .01% owned 99% of the wealth, and everyone else was pretty much equal. There could be a lot of mobility (it could be very easy for someone to move from the 10th to the 85th percentile if it only took an extra 20% of income to get there), but that level of inequality is still a major problem.
So these are two different issues and should be addressed as such. It's great if people have the same chance as ever of making it to the top tier in this country, but it is pretty disgusting for that top tier to be so far separated from normal people (even upper middle class) as they are. Two separate issues. Not really even linked.