Look, for a lot of reasons, I'm in the front row to knock Roger Waters down a peg or two. But fair is fucking fair here. This is cut and pasted directly from the site at that link:
It's not a replacement for the original which, obviously, is irreplaceable. But it is a way for the seventy nine year old man to look back across the intervening fifty years into the eyes of the twenty nine year old and say, to quote a poem of mine about my Father, "We did our best, we kept his trust, our Dad would have been proud of us". And also it is a way for me to honor a recording that Nick and Rick and Dave and I have every right to be very proud of.
That's not at all the same as saying "I'm re-recording this because it was all mine."
And by the way, if you watch that Classic Albums piece on DSOTM, I'm pretty sure it gives most of the credit for "Us And Them" to Rick Wright; the music came first, if I recall, and I think there was even a reference to the music inspiring the lyrics.