Analog modems achieve about 48kbps throughput with a 1200Hz carrier. This relies on trellis encoding.
For years this wasn't attempted because there was a textbook theory which stated that no comms channel could pass data at more then twice the carrier frequency. It was wrong.
Hmmm... Claude Shannon published his work on information theory and channel capacity in 1948. I'm not sure what textbooks after that period could have made the claim that datarate was limited by carrier frequency or channel bandwidth.
One should note that the paper was published in the Bell System Technical Journal and so widely read and discussed that Shannon became something of a popular culture B-list celebrity. There were articles written about the article, aimed at bringing much of the content within reach of more readers.
It is more likely that the limiting factor was the density and cost of the logic and A/D D/A converters at each end of the channel. To achieve high data rates on a voice grade channel requires a fair amount of resolution in time and amplitude. Both took a lot of power, space, and money before the advent of moderately high levels of solid-state integration. The need for some kind of forward error correction on high data rate channels makes the computational requirement even greater.
There were high speed digital links where the bitrate exceeded the channel width, and I'm sure there will be posters who can name a few. But before VLSI these were substantial chunks o' stuff and only justified where the need was compelling or potential profits outweighed the cost.
So, after 1948, any textbook that suggested a channel limit based solely on bandwidth was junk and not likely to have been respected or even read by people who built modems. Certainly the people at Codex, Racal, BTL, NASA, and a host of other places were well aware of the Shannon limit in the 50's and 60's.
To recap, Shannon showed that the channel capacity was proportional to the bandwidth of the channel and its signal-to-noise ratio.