I think they're confusing datacrunching power with color depth. A classic mistake.
And even if they were talking color depth, 16-bit is Thousands of Colors.
The SNES used a 16-bit (32,768) color limit with sprites having, at most, 256 colors on the screen at once(if they were one large graphic) or 16 colors per tile/sprite (15 plus mask).
The Genesis has 9-bit RGB palette (512 colors) with up to 61 colors on-screen at once... but I think there's also raster effects that can affect that value.
The NES only had a 16 color limit on the screen at once, out of a 64-color palette, withe tiles/sprites having three colors and a mask. Certain memory mappers developed later allowed the NES to do some nice trickery that allowed it to display more colors at once, even allowing instances in which the full palette could be displayed, though.
The GBA has a 15-bit color limit (that's 32768), I believe.
Color Depth is measured thusly:
1-bit = Monochrome (black & white, no grays)
2-bit = 4-color (in binary, a 2-digit number at most can have four values: 00,01,10,11) Old OLD Gameboy did this per layer and there were I think four layers (so there was still only four colors, green greener, greenest, black). Gameboy Color would add its own Four-color palette to each layer out of a 15-bit palette, making the Gameboy Color on par with the SNES in terms of color depth (though the GB games played in the system would inevitably only have 16 colors at most, Gameboy Color games enjoying fare more colors).
You can argue that the NES sprites/tiles palette was limited to 3 colors and a transparency, with the aforementioned 64-color palette, and 16 colors in the screen at once (from what I recall).
3-bit = 8-color (2 to the third power)
4-bit = 16-color (2 to the 4th power - most SNES and Genesis games followed this when it would come to the tiles/sprites... and I think GBA does this for sprites as well). It was a way to save space on the ROM cartridge, as smaller 'container' values would take up less space than large values.
In Windows95 and higher, you would have the option of having "High Color" (16-bit being 65536 colors), "24-bit True Color" (16,777,216 colors), and now most of us these days, with WinXP, Win7, and pretty much every new console and OS, use "32-bit" (4,294,967,296) color depth.