If you don't feel like reading The Colour of Magic & The Light Fantastic (the sequel that completes the story) then look for the DVD of The Colour of Magic (it originally ran as a double-bill made-for-tv movie, the first was CoM and the second part was LF).
There's also the Hogfather, a book released later in the Discworld universe, that got turned into a double TV movie. It is a much more faithful reproduction as they had more time, which in the case of the Hogfather was truly necessary.
Equal Rites, which came after that book, deals with this topic more directly. A seventh son has a seventh son...no wait, a daughter. She has raw magical power, and with some help gets to the wizard university. I'm not going to say any more; I don't want to spoil anything.
It is also worth noting that Equal Rites was published 1-2 years after this speech. Was Prachett trying to gauge the reaction to his satire by explicitly stating it?
I doubt he was thinking in those terms. More likely this was a concept that he'd already started to think of, and so the things he wrote about concerned things of that nature.
It's like how programmers designing registration systems become obsessed with talking about registration forms and CAPTCHAs. It's just where their minds dwell as they work.
Read "The Colour of Magic" if you get the chance, it's hilariously funny in spots, especially if you're a little bit of a fantasy geek.