Why can't Photoshop resize images correctly?

Question

This seems like a pretty basic function, but my copy of Photoshop can't do it right. Specifically, I'm using CS4, but I have a feeling that doesn't matter. I'd appreciate it if someone else would check to see if their copy of Photoshop works correctly either. Here's some quick step-by-step instructions to try it out:
Step 1 - Create a new file that is 4 pixels wide by 4 pixels tall. (Use basic options: 72 pixels/inch, RGB Color, Square Pixels, etc.)
Step 2 - Using the pencil tool, draw a red dot (1 pixel wide/tall) in each corner. So that the image looks like this:
Step 3 - In the menu, go to "Image" > "Image Size..." and increase the width and height of the image to 400 pixels using "Nearest Neighbor".
Now here's the image I end up with:
So we started with a 4x4 image, and now we have a 400x400 image. The math here isn't too difficult: 4 x 100 = 400. So each of our red dots in the corners should now be 100x100 pixels each. Simple enough, right?
Unfortunately, this was not the case for me. The red dot in the upper-left corner is now 97x97 pixels. The red dot in the upper-right corner is now 103x97 pixels. The red dot in the lower-left corner is now 97x103 pixels. And the red dot in the lower-right corner is now 103x103 pixels.
I guess Photoshop seems to think that both of the following statements are simultaneously true:
1 x 100 = 97
1 x 100 = 103
Am I alone in experiencing this buggy behavior? Or does everyone else get the same result? Is there some way to fix it?
Thanks for giving it a try!

Answer 1

I can confirm the problem here on Photoshop CS6 Extended x64 using Windows 7.
Adobe has never placed too much emphasis on getting things pixel-perfect in Photoshop - it is more fuzzy and touchy-feely philosophically.  This is not only illustrated by the problem noted above, but also by things like a selection made by a selection tool is often off by a pixel this way or that, paths snapped to things still don't *quite* overlap, etc.
They seem unwilling to change things that have been in the product a while, because apparently when they do so they inadvertently break other things.  And I can't say I blame them...  Given the apparent size of the code base and the extreme age of the software, I wonder what the development cost would be In order to fix something like this across the board, so that every operation really is pixel-perfect.  It might be the kind of thing that a complete redesign from the ground up is needed to fix.  Even then I guarantee you there would be problems.
To Adobe's defense, having been through the development of graphics software myself, I can authoritatively state that actually getting everything pixel-perfect is quite challenging in a world where computing can be done with integers or floating point numbers of various precisions, where no one can quite agree whether a pixel's coordinate identifies its center or one of the corners, where coordinate systems change depending on what subsystem you're using, and where OpenGL documentation recommends you offset your pixels by (0.375, 0.375) in order to ensure they align properly (no kidding).
-Noel