There is too little to go on in the book, so answers necessarily can be found only in the personal views of the author. Of which I can find nothing, unfortunately. So speculation time.
Assuming he did not research the topic that was a base of his idea I'd say he - as way too many people do nowadays - was told that RC Church was the main force of backwardness and only after it's power diminished the science and reason could flourish. I've always had the feeling that Pavane's world is somehow in crawl when progress is involved, and my assumption fits in it nicely. So steam engine was in development at the time of Spanish Armada (Jerónimo de Ayanz, a Spaniard, patented his steam machine in 1606), and it then steadily (albeit slowly) is improved to a steam engine...
But which assumption did not even saw truth in the farthest distance. For example, latest research suggest that English monks here and there were on the verge of Industrial revolution about 200 years before it actually happened. That would meant that severing ties with RC Church by England was the direct reason for that delay (as it abolished religious convents, which were left to rot and ruin. Who was in York in England knows that this was meant literally). I can go into details what exactly this involved and why it happened, as well as why the Industrial Revolution happened and once it started it still goes strong, but I don't think this is the place.
Back to the main thought. This is the pervasive theme in human "knowledge": that Catholic Church was anti-science. In my humble opinion if we had scientific standards Church had enforced back then we would not have the cesspool of false science and anti-human religion of science we have today. But this is my opinion only, so please do not start flame wars on that. Stick to the topic.
Which is: K.R. probably was told what was told and simply built on that. And glory to him for that.