If by “web safe” colors you mean the 216-color grid of 00, 33, 66, 99, CC, FF along each of the RGB axes (this is the common definition of “web safe” colors), then this basically incorrect. Web safe colors vary dramatically between displays, just like any others.
The reason for “web safe” colors was that most color displays in the mid-1990s used a 256-color palette to render everything on screen, so any colors not in the palette would be dithered. Browsers had their palettes set to include the 216 “web safe” colors in addition to various operating system default colors. Web safe is basically irrelevant to anything since sometime in the mid-2000s.
Web safe colors render just as inconsistently across uncharacterized displays as any other colors. And when the displays are properly characterized (“calibrated” is the popular word for this, but not quite technically right), colors at the very corners of the gamut (like FF0000 or whatever) are actually much likelier to vary, if any of the displays’ gamuts doesn’t cover the entirety of the sRGB gamut.
The reason for “web safe” colors was that most color displays in the mid-1990s used a 256-color palette to render everything on screen, so any colors not in the palette would be dithered. Browsers had their palettes set to include the 216 “web safe” colors in addition to various operating system default colors. Web safe is basically irrelevant to anything since sometime in the mid-2000s.
Web safe colors render just as inconsistently across uncharacterized displays as any other colors. And when the displays are properly characterized (“calibrated” is the popular word for this, but not quite technically right), colors at the very corners of the gamut (like FF0000 or whatever) are actually much likelier to vary, if any of the displays’ gamuts doesn’t cover the entirety of the sRGB gamut.