Calling something that can't do routing an "Internet" is pure hyperbole.
Without quantum routers, you can only do quantum key exchange with the router you're directly connected to. That router can only do quantum key exchange with things it is directly connected with. If any router on the communication path is untrustworthy... too bad.
If you want quantum crypto to be practical, you need routers that can redirect messages without measuring or copying them. That way you don't need to trust the network; only the endpoint you're talking to. (One possibility would be to setup dedicated circuits ahead of time, like the original telephone system, before qbits started being exchanged.)
Not sure if your beef is with the capital I or with the term "internet". Switching packets between multiple point-to-point networks is certainly within the realm of internetworking although I would agree that routing at layer 3 would come much closer to agreeing with a stricter definition of an internet.
In any case, it isn't really hyperbole unless you think they are drawing a comparison to the Internet (capital I).
Without quantum routers, you can only do quantum key exchange with the router you're directly connected to. That router can only do quantum key exchange with things it is directly connected with. If any router on the communication path is untrustworthy... too bad.
If you want quantum crypto to be practical, you need routers that can redirect messages without measuring or copying them. That way you don't need to trust the network; only the endpoint you're talking to. (One possibility would be to setup dedicated circuits ahead of time, like the original telephone system, before qbits started being exchanged.)