They didn't cover reel-to-reel recorders in that episode.
Obviously, recording the raw studio performances directly onto the masters that were to be reproduced would be a waste of resources. Multi-track reel-to-reel recorders were still pretty costly, even if the tape was relatively cheaper than the other costs of recording. That tech also improved up until the digital era, but I imagine most of the progress now goes into computer software.
People haven't really recorded directly to a groove in a plastic medium since wax phonograph cylinders. When you cut a vinyl master, you were probably doing it from tape.