Blank and Berez were definitely thinking about p-machines when they designed the Z machine, and there is a hat tip in the 1980 Creative Computing article describing its inner workings.
It's a review of three books, not a beginners guide to that period. I enjoyed and it made me want to read the books, so I guess it did its job.
It also contains a philosopher related pun which is either one of the best or worst I've ever heard. As great puns should be like that, it's probably the latter.
You can blame James I for that, not the BBC. Blasphemy was banned on the English stage in 1606 (the "Restraint of Players" act) and so later publications are usually expunged.
The BBC production could have been using a later edition (possibly based on the First Folio from 1623) which censors all the references to God and other blasphemy like "zounds", which is short for "God's wounds". You where almost certainly following along with an edition where the editor had restored the original published text from before the act was created.
[1]: https://mud.co.uk/richard/htflpism.htm