Extremely untrue. I've been slowly gathering pictures to illustrate a book I wrote for my daughter, and I promise you that just publishing it on the internet doesn't mean you relinquish rights to it. (I've been very careful to ask permission for all the photos - many of them from BYC). Publishing them does mean that sometimes it's hard to know someone is using it. If the image is linked to a place under your control, myself, I'd change it to a picture of a sick, starved, abandoned goose.
That actually isn't true...
If you post a picture on the internet, it belongs to everyone.