I am renting to you a box that is running a web-based application based on modified GPL components. The box only has inputs for the keyboard and monitor. Though you are running the application, you don't actually have the binary. Did I distribute?
What if I host the box for you in my rack?
What if you don't rent the box, but instead time-share access to it?
What if your only payment to me is your email address and permission to send you ads?
Congratulations, you've just defined "hosting a registration-required web site" as "distributing a binary".