You are renting me a box.
You are licensing me to use the box.
The box has a copy of the binary.
You have licensed me a COPY of the binary.
the GPL LICENSE applies. Other licenses do not supercede it.
Next.
Time-share is NOT distributing a binary, though. If your modified binary is being used, and the binary has not been copied, moved, lives, exists, or has otherwise been transferred, there is no distribution of said binary. It's only being used, and USE is NOT distribution, however you may want to redefine the word.