Exactly.

After all this discussion here my conclusion is that "connecting to the internet" is an ambiguous term.

It can mean "have IP connectivity, i.e., IP packets routed to and from the internet" in which case the described PC was not "connected to the internet with QMODEM". It didn't do anything IP.

It can mean "have a terminal that can interact with information from/to the internet" in which case the PC was indeed "connected to the internet with QMODEM".

To me, the second meaning is quite the stretch, but apparently to others it's fine.