Earlier quoted context omitted.
Sure, and you can absolutely use Photoshop, if you paid for it, and promise not to reverse engineer anything. Or, what do you think usage restrictions are or look like? If you don't share those modifications then you must not host that software such that it communicates with visitors; that's a restriction. The modifications that you are required to share cannot be any arbitrary modifications; anything you add has to…
Copyright covers four rights. The right to copy, the right to modify, the right to distribute, and the right to perform publicly. The GPL places restrictions on a combination of the modification and distribution aspect, which says that if you modify the software and distribute it, then you must also include source code. AGPL is more strict and says even if you just want to modify it and use it, you must supply the so…
If you've not modified the software, interested visitors can just get the source code from the same upstream, so why would it be required of you to host it.
However the following situation could arise and I don't see how the license addresses it. You visited a site running some AGPL service which was modified by those site operators. You decide to clone your own instance using their modified code. Since you're not modifying anything yourself you're not required to host that code. Now suppose that original site shuts down and disappears. The upstream for that modified code is no longer available. Are you on the hook for hosting it now? You've not modified anything yourself.