You're right. My description of Step 4 was incorrect. To achieve what Step 4 intended, read on...
[NB: I did manage to get the results I wanted (perfect alignment), but it's still a pain. The only reliable way I know of is to use the Direct Selection tool (white arrow) to pull each corner onto the grid (assuming the stroke has been set to inside the path). But new rectangles still don't snap to the grid, and dragging sides doesn't snap them to the grid either.]
However, it is possible to get new rectangles to start out with the stroke inside. This isn't related to the grid bug -- it's just a standard usage in Ai. The secret is to make sure "New Art Has Basic Appearance" is NOT checked. This checkbox is in the fly-out menu of the Appearance Panel.
To make use of the "New Art..." setting, click an existing rectangle that has the appearance you want. Then get the rectangle tool and the next rectangle will have the same appearance as the existing one. You can even make a little "palette" of pre-defined rectangles off to one side, and use each rectangle like a preset. With the rectangle tool active, you can just hold Ctrl/Cmd to click a preset.
This, of course, doesn't fix the larger rectangle pixel-alignment problem, but it's a very handy feature that does work consistently.
Thanks for pointing out my erroneous instruction. My apologies to previous readers of this thread!
