The Ur-Guru has kindly pitched in with some sources for the use of “the cloud” to mean the Internet. (He had the sense to look in more places than Wikipedia, which has a pretty confusing entry.)
PC Magazine has a dictionary entry defining cloud as a network infrastructure and showing a diagram using a cloud symbol, while Infovark describes the Internet as a cloud of clouds, with a pretty CGI rendering that looks like nothing so much as a star cluster. Certainly it’s not a nice, neat, geometric shape.
Just as you always suspected, the Internet is unruly, chaotic, and not particularly linear.