...if you can excuse my bracketed addition to your words, what you said there does seem to be part of "the spring" from which it bubbled up from.
It was all part of the Sola Ecclesia concept -- which had to be clung to at all costs. There was a great deal on the line. It was most assuredly about earthly influence, power and wealth too.
Some of the same can be said for some of those in the "Reform" camp also -- or perhaps more precisely could be said of some of those who were themselves fighting for freedom, and found they rather unavoidably were themselves fighting for political control and "power" over others, those persons taking up portions of "Reform" principles to oppose the political systems of governance (including taxation -- who was taxed, who collected the taxes, who received "share" of the taxes, those being split among various ranks of royalty & privilege, and the RCC papacy as personified by it's bishops, along the pope's Vatican too -- each of them getting some divy or another which came from the people) as much as(?) strictly theological issues.
Sound familiar?
Time for tea...
Though as wiki notes (and I do see the point);
Although some fans praise it as "one of his most playful and inventive songs" others criticize it for being "exactly the kind of cute self-indulgence that they find so annoying about his post-Beatles career." [13] Mason himself considers it "churlish" to be annoyed by the song, given that song isn't intended to be completely serious, and praises the "Hands across the water" section as being "lovably giddy."