Yes that is the copyright law. But there are limitations.... The Designer only owns the code.... Not the content of the web site. The content of the web site belongs to the customer (text, images, logo). The copy right law specifies what belongs to the designer and what belongs to the Customer. If you provide your designers with your own images... He can get in trouble for using them elsewhere.
Now what you can do is negotiate an "Exclusive" ownership with the designer.
Another thing that most designers are doing is charging you royalty fees for your sales on your shopping cart. The royalty fee can be for 1 to 5 years but no longer than that (and they have the right to go through your database/admin side to see all of your sales).
I wanted to add that this isn`t just for photos, websites and so on...if you have an idea for a new product and get someone with more technical expertise than yourself to develop the propotype from YOUR drawings etc...the act of interpretation and development may mean that that person has a right to be included on any patents that may come out of the project. I was personally `burnt` by this - i.e. someone`s father helped his son with the development of our prototype and when the product was a `hit` the father sued both the son and the company for his share! Nice!
Be careful to agree who owns what BEFORE undertaking the work - this also goes for people helping you with Business Plans and so on...they could always come back and ask for equity due to the addition of thier intellectual property i.e. ideas!