This looks interesting, but read carefully - while I haven't had the time to look at the article and the site in detail, it seems that it could be described as 'fringe science'...
I've actually seen a BBC Horizon documentary a while ago, "Do You Know What Time Is?" [http://www.bbc.co.uk/programmes/b00fyl5z], that also talks about this. On top of all the theoretical background, they interview people at the US Army that manage the GPS sattelites, and show how they have to resync the internal clocks every day because of this.
Oh, I don't doubt the effect, it's just that this article seems to have an anti-Special Relativity viewpoint, and espouses a different explanation for the effect. But I have just scanned it quickly.
The discussion of the twin paradox and SR seems to be lacking. There's a focus on only the time dilation effects and nothing on length contraction which would resolve the issue. Instead it becomes a mess of confusion.
Worth a watch if you like this kind of material.
EDIT: Sorry, I believe it was a different episode: "What On Earth Is Wrong With Gravity?" [http://www.bbc.co.uk/sn/tvradio/programmes/horizon/broadband...]
Here are the online video links to both episodes:
http://www.youtube.com/watch?v=V3aYKAJEVfQ
http://video.google.com/videoplay?docid=-421765295887486158