quantize() to a palette often chooses unideal color matches

What did you do?

I am quantizing many images to the same palette and colors are often not picked to be ideal values, instead being mapped to close values when an exact match exists in the palette.

What did you expect to happen?

Colors would be matched to the closest value in the palette or an exact match if one exists.

What actually happened?

Colors are mapped to close values. (Specifically white is mapped to #fcfcfc)

What versions of Pillow and Python are you using?

PILLOW_VERSION = '2.9.0'
VERSION = '1.1.7'
PYTHON = '2.7.10'

Please include code that reproduces the issue and whenever possible, an image that demonstrates the issue. The best reproductions are self-contained scripts with minimal dependencies.

import PIL.Image
ptext = '\xff\xff\xff\xfd\xfd\xfd\xfc\xfc\xfc\xfb\xfb\xfb\xfa\xfa\xfa\xf8\xf8\xf8\xf7\xf7\xf7\xf6\xf6\xf6\xf5\xf5\xf5\xf4\xf4\xf4\xf1\xf1\xf1\xf0\xf0\xf0\xef\xef\xef\xed\xed\xed\xec\xec\xec\xea\xea\xea\xe9\xe9\xe9\xe8\xe8\xe8\xe7\xe7\xe7\xe6\xe6\xe6\xe5\xe5\xe5\xe4\xe4\xe4\xdd\xdd\xdd\xdc\xdc\xdc\xdb\xdb\xdb\xda\xda\xda\xd8\xd8\xd8\xd7\xd7\xd7\xd5\xd5\xd5\xd3\xd3\xd3\xd1\xd1\xd1\xcf\xcf\xcf\xcd\xcd\xcd\xcc\xcc\xcc\xcb\xcb\xcb\xca\xca\xca\xc9\xc9\xc9\xc7\xc7\xc7\xc5\xc5\xc5\xc4\xc4\xc4\xc2\xc2\xc2\xbd\xbd\xbd\xbb\xbb\xbb\xba\xba\xba\xb8\xb8\xb8\xb7\xb7\xb7\xb6\xb6\xb6\xb5\xb5\xb5\xb3\xb3\xb3\xb1\xb1\xb1\xb0\xb0\xb0\xaf\xaf\xaf\xad\xad\xad\xac\xac\xac\xaa\xaa\xaa\xa9\xa9\xa9\xa8\xa8\xa8\xa6\xa6\xa6\xa5\xa5\xa5\xa3\xa3\xa3\xa2\xa2\xa2\xa1\xa1\xa1\xa0\xa0\xa0\x9d\x9d\x9d\x9c\x9c\x9c\x9a\x9a\x9a\x99\x99\x99\x94\x94\x94\x91\x91\x91\x8f\x8f\x8f\x8d\x8d\x8d\x8b\x8b\x8b\x87\x87\x87\x86\x86\x86\x85\x85\x85\x83\x83\x83\x80\x80\x80~~~}}}|||{{{zzzwwwvvvtttsssrrrpppooolllkkkjjjfffeeedddcccbbbaaa```___^^^\\\\\\YYYXXXWWWUUUTTTSSSMMMLLLKKKIIIHHHGGGDDDCCCBBBAAA@@@???>>>===<<<;;;:::666444333222///...---+++***)))\xd8\x08\x00\xd6\x08\x00\xd5\x08\x00\xd4\x08\x00\xd2\x08\x00\xd0\x08\x00\xcc\x08\x00\xcb\x08\x00\xca\x07\x00\xc9\x07\x00\xc8\x07\x00\xc6\x07\x00\xc5\x07\x00\xc4\x07\x00\xc2\x07\x00\xba\x07\x00\xb7\x07\x00\xb6\x07\x00\xaf\x06\x00\xae\x06\x00\xad\x06\x00\xac\x06\x00\xa9\x06\x00\xa0\x06\x00\x9e\x06\x00\x9c\x06\x00\x94\x05\x00\x93\x05\x00\x92\x05\x00\x8c\x05\x00\x8a\x05\x00\x89\x05\x00\x88\x05\x00}\x05\x00y\x04\x00r\x04\x00q\x04\x00o\x04\x00d\x04\x00b\x04\x00a\x04\x00^\x03\x00V\x03\x00U\x03\x00R\x03\x00Q\x03\x00K\x03\x00J\x03\x00H\x03\x00G\x03\x00F\x03\x00A\x02\x00@\x02\x00=\x02\x00<\x02\x00:\x02\x00(((&&&%%%!!!\x1f\x1f\x1f\x1e\x1e\x1e\x1d\x1d\x1d9\x02\x008\x02\x002\x02\x001\x02\x00,\x02\x00+\x02\x00*\x02\x00(\x01\x00$\x01\x00#\x01\x00"\x01\x00\x1f\x01\x00\x1c\x1c\x1c\x1b\x1b\x1b\x1a\x1a\x1a\x19\x19\x19\x18\x18\x18\x17\x17\x17\x15\x15\x15\x14\x14\x14\x11\x11\x11\x10\x10\x10\x0f\x0f\x0f\x0e\x0e\x0e\r\r\r\x0b\x0b\x0b\t\t\t\x08\x08\x08\x19\x01\x00\x16\x01\x00\x07\x07\x07\x06\x06\x06\x05\x05\x05\x04\x04\x04\x03\x03\x03\x02\x02\x02\x01\x01\x01\x0b\x00\x00\x08\x00\x00\x07\x00\x00\x06\x00\x00\x05\x00\x00\x04\x00\x00\x03\x00\x00\x02\x00\x00\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00' #Palette is not malicious, similar behavior occurs with white on many palettes.
i = PIL.Image.new('RGB', (1,1),(255,255,255))
p = PIL.Image.new('P',(1,1))
p.putpalette(palette)
p.putpalette(ptext)
i2 = i.quantize(palette=p)
i2.show()

Start by running the supplied one-pixel reproduction against PIL.Image.quantize() and inspect the quantization path it exercises. Confirm that an exact palette color such as white is selected when present, while nearest-color behavior remains correct for other inputs.