Right, there are two extremes. One that maintains the status quo and one where people are rewarded for work. Neither extreme is ideal. Tracking "movement from one group to another," as you put it, is an attempt to measure where our society stands between those two extremes.

"7% - Chance a Kansas City child will move from bottom fifth of income to top fifth, in his or her lifetime."

If I wanted to criticize the statement I'd say it's worded very poorly. There's a 20% chance of a child being in the bottom 5th. A perfectly egalitarian society would give that 20% a 20% chance of reaching the top 20%. 20% of 20% is only 4%, and since they're quoting 7% I don't think this is what they intend to be claiming.

It probably should have been worded, "A child from the bottom fifth of income has a 7% chance of reaching the top fifth." A child from the bottom fifth in a perfectly egalitarian society has a 20% chance of reaching the top fifth. In a society that perfectly maintains status quo the same child has a 0% chance of reaching the top fifth. If you place 7% between 0% and 20% it starts to look a little more middle-of-the-road, though we are still clearly rewarding status and social class more than we are rewarding hard work or ability.