Isn't it the opposite of the headline? Modems were hamstrung by digital phone lines you didn't know we had. One final trick allowed them to match, but not exceed, those digital lines.
While today you'd probably expect that the IP network could connect to every phone branch office where the local loops were connected to the phone network, that wasn't necessarily the case - Internet data would usually have to travel some of its way over the phone network backbone, with the problematic digital encodings. V.90 and related standards allowed the phone network to accept the digital data directly from ISPs and send it in digital form to the branch office, without attempting a digital to analog to digital conversion to inject it as digital voice into the phone network. That's why the upload speed couldn't be improved via this method - it would still need to undergo analog-digital conversion to travel across the phone network to the ISP where it could enter the IP network. (V.92, a later standard, improved upload speed to 48 Kb/s via fancier signal processing trickery that could survive the digital voice conversion.)
The phone companies had enormous sway over the development of these longer haul protocols. The debate around packet sizing almost always favoured smaller cells (especially ATM), which was more ideal for voice - with the added overhead for more standard IP packets. They were also often very connection-oriented, with all the extra equipment overhead required.
But if it was a direct copper pair end-to-end then attenuation and electrical other characteristics would have made it hard to achieve the higher speeds, this is the Shannon limits they mention.