Did you watch the video? He says "creating", as it says in the Snopes link. It's not a brilliant wording, but it's a reasonable misstatement.
Also, I think it's clear that most people use "create" and "invent" as synonyms most of the time, especially when the object being invented or created is one-of-a-kind (which is believed to be true for the internet by most of the public, though it isn't strictly true).
So, when someone says, "Al Gore says he invented the internet" and you say, "No, he said 'took the initiative in creating the internet' ", that someone is likely to say, "Why say 'no' if you're going to agree?"
We're all familiar with false popular memes that spread faster than they can be stomped out: You only use 10% of your brain. Al Gore said he invented the internet. Perhaps it doesn't surprise you that some memes in popular culture can't be killed. But does the same thing happen in science?
Most of you have probably heard of Broca's aphasia and Wernicke's aphasia. Every textbook and every college course on language and the brain describes the connection between damage to these areas, and the speech deficits named after them.
Also, both are probably wrong. Both areas were mistakenly associated with their aphasias because they are near or surrounded by other areas which, when damaged, cause the aphasias. Yet our schools continue teaching the traditional, erroneous story; including a lecture in 9.14 at MIT given in 2005. Both the Wikipedia entry on Wernicke's aphasia and the Wikipedia entry on Broca's aphasia are still in error; the Wikipedia entry on Wernicke's area has got it straight.
Is it because this information is considered unimportant? Hardly; it's probably the only functional association you will find in every course and every book on the brain.
Is it because the information is too new to have penetrated the field? No; see the dates on the references below.
In spite of this failure in education, are the experts thoroughly familiar with this information? Possibly not; this 2006 paper on Broca's area by a renowned expert does not mention it. (In its defense, it references many other studies in which damage to Broca's area is associated with language deficits.)
So:
References
Bogen JE, Bogen GM (1976). Wernicke's region—Where is it? Ann. N. Y. Acad. Sci. 280: 834–43.
Dronkers, N. F., Shapiro, J. K., Redfern, B., & Knight, R. T. (1992). The role of Broca’s area in Broca’s aphasia.
Journal of Clinical and Experimental Neuropsychology, 14, 52–53.
Dronkers NF., Redfern B B., Knight R T. (2000). The neural architecture of language disorders. in Bizzi, Emilio; Gazzaniga, Michael S.. The New cognitive neurosciences (2nd ed.). Cambridge, Mass: MIT Press. pp. 949–58.
Dronkers et al. (2004). Lesion analysis of the brain areas involved in language comprehension. Cognition 92: 145-177.
Mohr, J. P. (1976). Broca’s area and Broca’s aphasia. In H. Whitaker, Studies in neurolinguistics, New York: Academic Press.