I am certain this is not true, as I only use them for a subdomain CDN for hosting my static site, and don’t use them for any of my other dynamic sites that are on the same parent domain.
Maybe what you say was true at one point. I only set up a static site and used Cloudflare to front it within the last couple of months.
When I set it up a couple of years ago, it was a hard requirement and looking at their features, it still seems to be the case: https://www.cloudflare.com/plans/#overview (under 'Custom Nameservers')
When I tested a while back, I couldn't setup a subdomain in cloudflare, it only allowed me to setup the root domain. When I did this and just updated the NS records for the subdomain to point to cloudflare, their validation of the nameserver change never passed (since I only set NS records on the subdomain level).
I'm not trying to argue for arguing sake, just trying to show why I thought/said what I originally said :)
Honestly, if this does now work, or there's a way around it, I'll be really happy as I could switch a couple of subdomains to them :D
Though, just a note that if you use them, you need to use them as your nameservers for your domain (the whole domain) (at least for the free tier)
... maybe doesn't matter for most people, but something that's put me off massively :D