Only partly true, Anachronism. (First of all, of course, immediately upstream of Glen Canyon Dam, "the river" is Lake Powell.) Glen Canyon Dam, as you described, does indeed trap tons of silt from the Colorado River--that's what it was originally built for, as I understand it, in order to extend the life of Lake Mead and Hoover Dam downstream. The water does flow out of Glen Canyon Dam clear and green. But it is still fairly rare to see the Colorado River looking green as it does farther downstream in Goldmember's pictures. Rain on the plateaus high above the river flushes more mud down through the many streams and rivers that enter the Colorado downstream from the Dam--particularly the Little Colorado River--typically turning the green water from the Dam back into the chocolate-milk-like flowing mud you see in most pictures of the River.
I'm not sure about that- Google image search shows quite a lot of green... https://www.google.com/search?q=Grand+Canyon+colorado+river&source=lnms&tbm=isch&sa=X&ei=N3SbU9TdEsKSyATXuoLYBg&ved=0CAYQ_AUoAQ&biw=973&bih=762
Contrast with a search for Cataract Canyon flowing into Lake Powell... https://www.google.com/search?q=Grand+Canyon+colorado+river&source=lnms&tbm=isch&sa=X&ei=N3SbU9TdEsKSyATXuoLYBg&ved=0CAYQ_AUoAQ&biw=973&bih=762#q=cataract+canyon&tbm=isch
Upstream silt capture was a side benefit, but the key reason Lake Powell exists is to allow states on the upper Colorado River to pull out water upstream while maintaining their contractually mandated flows to the lower river states per the Colorado River Compact. Before the dam, upper states had no good way to retain water for their use while still delivering water to AZ, NV, CA. Very little water gets pulled from Lake Powell, it just gets parked there in an incredibly hot place to evaporate ridiculous amounts of it away, just to satisfy terms of an agreement that assumed far more river flow than really exists... Of course, the crazy idea of having water sit for years in a desert just to have a sizable chunk of it evaporate away also holds for Mead, but at least Las Vegas actually pulls water out of Mead...
The dividing line between upper and lower is Lees Ferry just below Glen Canyon Dam, one of the big (but not only) reasons Lake Powell happens to be where it is.