Thus far, this is true. The global phone system has persisted for almost 100 years, evolving via numerous “gateways” to older iterations of system (e.g. land lines -> cell phones, copper wires -> microwave links -> fiber optic lines, in-band signaling -> out-of-band signaling, individual lines -> multiplexing, etc.)
Yet despite the same phone system evolving and persisting for almost a century, dial-in BBSes, Minitel [0], and other outdated technologies that use phone lines are completely dead. Just because a communications medium may persist for a long time doesn't mean protocols utilizing the medium will.
I think that's the important nuance: humans have always had a keen interest in keeping records of history. We are at an early age of electronic computers, but we've already got things like archive.org — that's likely to persist in some shape or form, just like we are actively trying to persist books and movies from different eras.
Other than natural or civilizational catastrophes, I only see the risk in the amount of data needing storage surpassing any one's entity ability to archive it, but I am sure "humans" would deal with that in due time too.
Edit: I do not necessarily believe the torrent claim, but wanted to clarify why I see a point in it.
Assuming we can always hook up another gateway to the next “internet” is like someone 500 years ago assuming that they could send a message via horse to the internet.
The old internet could disappear as long as the economical incentives are enough to transition to a new centralized form of internet.
We are far from it, thanks, but don’t neglect that Facebook made a ton of websites become useless (to their owner at least) and disappear. Also, networks operators have made low cost plans limited to some of the internet. This is far from enough to kill the internet but a more restricted network is totally amongst the possibilities. And I’m not even talking about state control like in China.
