Digital BW, The Print

I am puzzled by something I stumbled across yesterday.  I was working up an image 
converted to B&W with Channel Mixer (60% Green, 40% Blue).  I wanted to sharpen the 
image and tried a variation of the Smart Sharpen/Reduce Noise Sharpen action I use - 
specifically I copied the image, converted it to Lab Colour Mode (flattening in the process) 
and only sharpened the L channel.  I made a mistake while doing this and brought just the 
L channel of the copy over to the original as a layer.  This revealed something I found 
surprising:  the Lab Colour copy ( a flattened greyscale image) had luminance information 
in the a and b channels.  That is the luminance of the L channel alone was different from 
the luminance when all three (L, a and b) are displayed.  This would seem to fly in the face 
of what I thought the a and b channels represented.  

I did another quick test.  I took the RGB original with the Channel Mixer layer and flattened 
it, leaving a greyscale image in RGB.  Converted it to Lab.  If I uncheck either one of the a 
and b channels the image stays looking the same.  But if I uncheck both the a and b 
channels (leaving just the Lightness channel displayed) the luminance of the image 
changes significantly.

I must be missing something basic but I don't quite get it.... Ideas?

Steve

PS:  I am using PS CS2.  (My RGB space is ProPhoto RGB.)