Actually, no. You may use GPL'd code any way you like (that's freedom 0) and share with others (freedom 2). You can likewise modify the software any way you like (freedom 1). And all this time, you need not release source code. The condition to release the source only kicks in with freedom to distribute your changes (freedom 3), so only when there is a third person involved with your derivative you have to grant them the same freedoms you've been given by the original author.
In fact, this was a problem with SaaS: You could've modified free software, and run it in the back on your servers, and say that you're simply providing a service to the end user, and since he's not getting the modified program, he doesn't get to have its source either. This is what AGPL is designed to address, and thus it's mostly used for web software. So with AGPL, as soon as you use a program, whether you have a copy, or are executing it online, you get access to the source.