Yes, it is true that the color temperature of plain tungsten lamps does vary with wattage. Lower wattage lamps burn cooler, and therefore produce warmer light. So as you drop the wattage, the light gets redder, which requires even more color correction to make it work with daylight.
That's why I relit the scene with 5000K LED bulbs when I wanted to do available light color photography. It was easier to relight the scene and shoot with high speed film than it was to figure out how blue a filter I needed, plus I could shoot handheld! Admittedly, one can't always relight the scene, but for what I was trying to do, this was the simplest approach, and I didn't have to use ISO 5,000,000 film! Plus, negative film gives you the opportunity to do some small corrections "in post" after getting it mostly right in-camera.