Let's say I have a web service that links to a C library which is licensed under GPL. If I host this service on my own server, then I think I don't have to license my web service under GPL. This is probably the major difference between GPL and AGPL.
However, what if I host it on Amazon AWS? When my service is hosted there, although I own my cloud instance, the instance is on a server owned by Amazon. This means that an Amazon server contains a full copy of my web service. Does that mean I 'distribute' my work to Amazon AWS? If so, does this mean any third party also have rights to get a copy of my source code (the first paragraph of this FAQ item seems to suggest so)?