Ok... here's how I understand it to work... (Warning : May be totally incorrect).
Shaving does not make your hair thicker.
What it does do, is gives your hair a "blunt" tip (that does not reflect the light as well) instead of the fine, tapered tip it would normally.
That's why shaving an area you aren't used to itches when it grows in (until the skin in the area toughens up).
Also, in an unshaven area, only some of your hair is at full length at any time. Some has "fallen out", some has yet to grow above skin level, some is short, etc. It all grows at different rates.
You shave, then all the hair will appear to grow in at once (instead of "in stages" as it normally would). This can make your hair appear thicker - but a month or so without shaving will undo that.
Again, this is just what I've heard.