"In the Internet" vs. "on the Internet"
I would always use "on". At least if you are talking about the contents you can find on it. If you're talking about its hardware structure for instance, then, "in" can maybe fit in some cases, I guess.
I suppose the large number of "in" prepositions in the phrase can be explained like this: in many languages, including Russian we use the preposition which can be translated into English as "in". So what people often do when they don't know what the correct way is - they "copy" exactly as it's told in their native language. I guess the number of native speakers who use the Internet is much smaller.
If you're talking about information retrieved from the Internet, people routinely say "it is stored ON the Internet", "I found it ON the Internet", "information ON the Internet is ..." etc.
The only example I can think of where you would use "in" would be a phrase like, "I am interested in the Internet".
As noted in response to AmiroucheDouda's post, you might use "in" when "Internet" is used as an adjective to modify some other word. Like, "We live in the Internet age", "In an Internet-based system, access is ...", "Thinking in Internet terms ...", etc.
'On the internet' would refer to data/items/websites that one can find there. as Pierre said, the 'Internet' can also be seen as a web of hardware elements like routers and switches.
that switch is 'in the internet'