Color meters were never designed to be used to measure light sources with a broken spectrum. How much should we trust them?
The typical color meter has three sensors that measure specific wavelengths of red, green or blue. The assumption is that all three of these wavelengths will occur naturally in a black body radiator, which is a theoretical source that radiates light across all wavelengths and changes color temperature as it is heated. When we talk of a 3200k or 5600k light source, what we're referring to is the color of light emitted by a black body radiator that is heated to 3200k or 5600k. It's true that 3200k light is warmer than 5600k light, but that doesn't mean that the black body source has stopped radiating at certain wavelengths. What has changed is that some wavelengths are being radiated more than others--in the case of 5600k light, more blue is being emitted than red, but red is never completely eliminated.
The problem with broken spectrum sources is that certain wavelengths ARE completely eliminated. The typical flourescent light has huge green and orange spikes, with not a lot else going on. Using a color meter with these sources can result in faulty correction, as colors are typically presented as ratios (orange to blue, green to magenta) and one half of the equation may not be present.
One of my gaffers says that he only ever uses half the gel correction his color meter recommends. Another of my gaffers uses two-thirds the recommended correction. Both techniques seem to work well.
HMI's read reasonably accurately--or at least their spectrum is intact enough that the average color meter suggests gel correction that works.
Certain RGB LED sources--such video displays created by Element Labs: STEALTH or VersaTUBES--emit a broken spectrum but the RGB wavelengths seem to correspond to the wavelengths measured by the average color meter. Adjusting the white point of such a display, using a Minolta Color Meter 2, works quite well.
Keep in mind that different imaging tools will see a broken spectrum in different ways. Film is much more sensitive to blue and green, which is why flourescent lights will photograph with a severe green/cyan cast. The same lights seen through an HD or video camera may appear fairly neutral. They may look a touch green, but nothing that can't be easily corrected. A typical three-chip camera doesn't have the same wide gamut that a film stock does, so it won't see certain colors as strongly. In such a case, color correction that works for film may be overkill for a digital imager. Fortunately, when shooting digitally, we can often see what we're doing.
Color meters are very useful but not always reliable. It's not their fault--they weren't designed to measure the kind of crazy energy-efficient light sources currently foisted upon us. Beware, and when possible test, test, test!