My understanding is that Google would also see the 403 error page, just as it does for a 404.
The idea of this is that either the site owner will remove the link (because they will not want broken links) or that Google will eventually de-ındex it as it will 404's. But as I said earlier, if Google does not crawl the page where the link is located it really doesn't help from that point of view.
But should the site put up any further links to mine, Google will not be able to follow them and therefore I can at least prevent it from happening again.