> Well, it's ours.
No (t really).
> We created it.
Yes (mostly, originally).
> We've allowed other countries to use it because it benefits us to do so.
It is a distributed network. It is composed of pieces owned by different principals, content created by different people and code and technology contributed by the entire world. If the U.S. were to close its internet today, and block any connection to the outside world, it might crash the web for days or weeks, but after that, the dependencies on U.S. controlled infrastructure would be quickly replaced, and the U.S. would be left with a national intranet, while the rest of the world would have the Internet. Hell, even for DNS, which is the specific system in question here, it is not so much "the U.S. owns DNS" but "a large number of DNS servers, owned by different parties, have pretty much agreed to replicate the U.S.'s version of the DNS registry and trust it as authoritative". They could be set to replicate a root DNS server in Geneva, Brussels or even Beijing within hours. In some ways, other countries allowed the U.S. to dictate how domains are assigned because it benefits them to do so (and because ICANN has been for the most part a trusted arbiter of the DNS system).
I am not even in favor of a U.N. controlled Internet, based on what I know is likely to happen if this move occurs now (the U.S. is, depressingly, among the least Internet-hostile countries in the world right now... and it is hostile enough). I actually like ICANN and how they do things, for the most part. "If it ain't broken don't fix it" and all that. But this whole "we own the entire Internet because it started here" sentiment is as ridiculous as if, say, China were to claim that they own all of the world printed money because they invented paper money originally.