While writing my last post, I found out something interesting: Google Blogger strips out the GPS EXIF tags when you post it to your blog while leaving the rest intact.
Here's the exif data of the pic I posted yesterday - all of it identical to when it was taken.
And just to make the situation more complex, I can go and have a look at the uploaded photos in picasa - and it shows the gps data as being intact!
So google doesn't modify the original at all, but will quietly rip out GPS data from any copies that are displayed publicly. This is a pretty useful safety feature. With it, I can just upload any picture without worrying that I'm giving away where I live or work.
It's confusing that I can't find this feature noted anywhere. It's the kind of subtle but important feature that shows a product has been carefully thought out and sets it apart from the rest, but neither the help documents nor my frantic googling found a single reference.