Indeed, so much of this stuff was created with an expectation of tungsten light, with its CRI (Color Rendering Index) of a perfect 100.
I fight with this a lot as a digital video guy. Digital sensors are generally tuned to expect 5200k daylight. The bizarre color from fluorescents, LEDs, HIDs, even HMI lighting - a lot of gels required to get everything even. Shooting stills, hell - a couple Speedo packs and it's F16 at ISO 100, nice clean daylight. Get into motion work with digital sensors, and you need a pretty big budget to just assume your color will be clean and hopefully shoot under ISO 1000.
I'd be curious to see if an LED source could be gelled to work reliably with standard contrast filters. Since the contrast grades are essentially color correction gels, it **seems** like it would work. But there are bizarre spikes of green or yellow in what is being sold as "daylight" sources these days. I have some pretty strnage gel combos on set.