In the doc page for Binarize (under Details and Options), is this statement: Binarize works with 2D and 3D images. It converts multichannel and color images into grayscale images, then produces an image in which every pixel has value 0 or 1.

Interestingly, this statement is not completely accurate, as my function below demonstrates. But at least the behavior for Binarize makes more sense than the ColorConvert to "Grayscale" evaluation. I'd argue that the latter implementation is a bug.

In[98]:= binComp[imageData_List, thresh_] :=
 Module[{im, im2},
  im = Image[imageData, ColorSpace -> Automatic, Interleaving -> True];
  im2 = ColorConvert[im, "Grayscale"];
  ImageData /@ {Binarize[im, thresh], Binarize[im2, thresh]}
  ]

In[99]:= binComp[{{{1, 1, 1, 0, 0, 0}}}, 0.5]

Out[99]= {{{0}}, {{1}}}

In[100]:= binComp[{{{1, 1, 1.001, 0, 0, 0}}}, 0.5]

Out[100]= {{{1}}, {{1}}}

I argue that this evaluation is a bug:

In[102]:= 
ColorConvert[
  Image[{{{1, 1, 1, 0, 0, 0}}}, ColorSpace -> Automatic, 
   Interleaving -> True], "Grayscale"] // ImageData

Out[102]= {{0.5925}}

Thanks for your input. Your objections are certainly valid!

One additional interesting evaluation is to observe the conversion of a 2 channel image to RGB

im = Image[{{{1, 0}}}, ColorSpace -> Automatic, Interleaving -> True];
im2 = ColorConvert[im, "RGB"];
ImageData[im2]

{{{0., 0.707106, 0.707106}}}

Okay, I have no idea why that formula is used. Pretty interesting.

And, finally, when an image with automatic colorspace is displayed in a notebook, the same computations that we see in ColorConvert[-image-, "RBG"] are used. Here is one way to show that (I don't want to upload an image here):

In[33]:= Rasterize[im, "Image"] === Rasterize[ColorConvert[im, "RGB"]]

Out[33]= True