More likely the other hybrid film he’s referring to is Song of the South, especially as Pete’s Dragon was released six years after Bedknobs and Broomsticks. Then again, I’ve only seen bits and pieces of that film so I don’t know exactly how much animation is in that film.
I don’t recall The Black Cauldron reusing any backgrounds (would the backgrounds from the two films mentioned have even been compatible for Technirama), but it does reuse some animation from Sword in the Stone for the scene where Taran loses Hen Wen.
I also recall reading that the tracks for Deems Taylor’s narration had badly deteriorated, which led to the redubbing.
As far as Taylor’s credentials, it turns out he was also a bit of a film historian as well. I have a book he wrote covering the dawn of film up to the year after Fantasia was...