I heard someone tell me today that if you have the color cranked up too high, you can damage a CRT.

Not sure how that's true, but just want to pick at your brains for a moment on this.

When for example, I look through a color bar generator, and crank up colors high, and look through a red filter, I DO notice that the color red is brighter than white. This would lead me to believe red is in fact putting out more intensity than the red gun is on white. Perhaps there's some truth in this?

Not any acute damage, just the normal warning about not leaving a fixed pattern on for days at a time, which will burn a pattern into the phosphors. It is quite normal for NTSC sets to have the red gun have more intensity in the red bar than the white bar. This is part of the matrix design that (approximately) compensates for the yellow caste in the sulfide green phosphor. (Extra gain in the R-Y turns off the red more for greenish colors, but it also turns the red on more for red colors.)

I doubt that it'll hurt the CRT to run it with the color too high unless it's also being driven at a higher brightness, (maybe if the color is so high everything is just glowing blobs of color it might be detrimental) running it at high brightness will wear a tube out faster just like running a car engine harder will wear it out faster.
It's harder on the both the Phosphor and the Cathode.

There was a warning relating to something like this in the black RCA color tv manual from the 50's that featured the 15G'. If I remember correctly, it was in the setup section.