Oh, bother. Don't you people know familiarity when it comes around? When people say that they "have the internet," they know that they don't (well, most of them).
I'm not an internet noobie by any means, but when I go to a friend's house for a LAN party, I say, "I've got the internet" when it's true.
Let me clarify, I say, "I've got the internet" when the proper phrase of "my computer has an established connection allowing access to the collection of data and computers known as the internet" is true. Which would you rather say? It's not ignorance, but ease.
Do you give people slaps on the wrist when they say "I have cable TV"? Of course not. It's obvious that, while they're technically saying that they own various lengths of usually flexible stuff, they mean something entirely different.