Actually it is the opposite. If you have Messages in iCloud, they do not store messages in "iCloud Backup" but keep it separate with some client-side device-to-device encryption key (UPDATE: which they also store a copy of inside iCloud backup unless ADP is on; thanks to 'modeless). If you enable iCloud Backup and Messages in iCloud is turned off, it will backup all your messages in a way visible to Apple servers. Of course, that is unless you enable Advanced Data Protection (the thing that UK hates).
The fact that this is so unintuitive that I had to explain it and I am only 95% sure I got it right is precisely the problem.