It's a pretty hollow platitude though. It describes nothing. I for one think that in 4e the action flows and the rules serve the gaming group, rather than the other way around. But there are people (you included if I remember correctly) who would strongly disagree with this. The real lesson to learn is that one size doesn't fit all when it comes to RPGs, rather than making some appeal at edition warriors.
(Trying very hard not to be edition warring here; let me know if I haven't been successful, please)
I think the only real big issues with 4e are that it was - while a great game and very successful in being what it wants to be - not suitable for a notable proportion of the existing D&D market when it was released.
By "Not suitable", I mean that the mechanics and dynamic in play are very different to any previous edition. Some people love them, but some people do not. WotC's error here was in misjudging their market, expecting that most people would either like the new system or not mind the changes. This is a significant error, and if the system itself hadn't been as sound as it is the whole situation could have been much worse for them.
I've been GMing two 4e campaigns since 2008. One is a regular game with five players, none of whom had played any tabletop D&D before. The other is an irregular give-the-other-GM-a-break game with a very experienced group that plays 3.0 the rest of the time, and has done since around 2002. I've never actually played 4e myself, even though I've run it for about six years now

Both of those games are going to convert to 5th edition this year for different reasons. Partly it's because I find 5e easier to GM than 4e, but mostly it's because the new edition serves the two groups (specifically) better than 4th. About half of the experienced group of 3e players are of the "4e isn't enough like D&D to me" persuasion. Not enough to stop playing, because they've apparently been enjoying the game I've made for them, but enough that they suggested converting after I ran a few playtest sessions up there and mentioned I found it nicer.
I think one, maybe two people in the other group would be absolutely fine with 4e in any form - they both spend more time working out mechanics than the rest. However, that group also has a barbarian who has issues choosing which rage to take. She vastly prefers the conversion of her character into 5e we created to test the process, because it's much simpler and easier to work with while preserving all the things she likes.
I think it would help a lot if we played more often - 2013 has been pretty difficult for several of us, and we only get together once a month at best. However, the last session we had multiple bits where everything was brought to a halt because one player or another couldn't find something on their (up to) 10 page character sheets.
None of the above is a serious issue with 4th edition, but it *is* an issue with 4th edition not serving the two groups I play with, in the specific circumstances that we play. Other groups will be very different. To be honest, I'd absolutely love giving 4e a try in a regular game. But as it stands right now, I'm much more likely to get a 5e game. None of my 3.0e group ever talked about running anything in 4e, but after the last session I ran up there both of the other two GMs were considering it (and one of them was considering moving a 3.0e game to it).
TL;DR:
4th edition was great, but anecdotally I can see that it may not be as widely suitable to the D&D market as a whole as 5e or previous editions. Which is sad for 4e, but doesn't detract from it I think.
So to actually make a conclusion, finally: I can see what Sage Genesis means, but I *do* think that 5e is better at serving a wider proportion of the D&D market than 4e was. We'll see in a few months if that's actually true, of course...