Here's the APOLLO web site, authored by Tom Murphy, APOLLO project director:
http://physics.ucsd.edu/~tmurphy/apollo/apollo.html
The Wiki discussion page is short and simply says that Tom Murphy gave permission to use that page and the team's papers to create the Wiki article. So the "apparently well-informed wikipedian" (user Lou Scheffer) is using that.
We see the purpose of APOLLO is to probe gravity to even greater precision, plotting the motion of the moon to an unbelievable 1mm precision. As the project page and papers indicate, quantum gravity notions (as well as many alternate theories of gravity) predict some violation of the Equivalence Principle (EP) in various forms in some regimes. These will be very, very tiny (IOW, if GR is not right, the replacement theory of gravity must very close to it in all regimes we've probed), hence the need for incredible precision.
An example of a supposed EP violation was the recent hubub over some apparent time delay in receiving very high energy photons (TeV, IIRC) relative to lower energy photons from some distant source. IIRC, the delay would be a minute or so relative to billions of years of light travel time.
If so, that is an EP violation -- the TeV photons follow an every so slightly different path through space-time than lower energy photons.
So yes, this is the mission of APOLLO -- probe gravity to even more precision. It is way, way, way, way too early to draw any conclusions based on their first runs.
I want to readers here to understand we're talking mm levels relative to the moon's distance from the earth. That's just amazing. The way Jerry worded that made it sound like there was some big difference in the moon's trajectory vs GR predictions, ie the moon zigged when GR predicted it would zag.
-Richard