False. U.S. Copyright law is quite explicit that the making of what are
called "derivative works" -- works based or derived from another copyrighted
work -- is the exclusive province of the owner of the original work.
This is true even though the making of these new works is a highly
creative process. If you write a story using settings or characters
from somebody else's work, you need that author's permission.
Yes, that means almost all "fan fiction" is arguably a copyright violation. If
you want to publish a story about Jim Kirk and Mr. Spock, you need Paramount's
permission, plain and simple. Now, as it turns out, many, but not all
holders of popular copyrights turn a blind eye to "fan fiction" or even
subtly encourage it because it helps them. Make no mistake, however, that
it is entirely up to them whether to do that.