My guess would be that many of the references you call do in fact work for companies with a no-reference policy. This has at least been the case at all of my employers (large and small places alike, some household names), save a 5 person startup.
In my experience, although near-ubiquitous a no-reference policy mostly seems to mean "if anyone calls the company line or shows up on prem, we redirect them to HR who then tells them nothing". It doesn't mean they go out of their way to stop individual employees from giving positive references on their own time (to wit I've never seen any employer actually make any effort whatsoever to disseminate their no-reference policy to employees, it's just a CYA measure they adopt if communication happens through channels they're directly accountable for)
In my experience, although near-ubiquitous a no-reference policy mostly seems to mean "if anyone calls the company line or shows up on prem, we redirect them to HR who then tells them nothing". It doesn't mean they go out of their way to stop individual employees from giving positive references on their own time (to wit I've never seen any employer actually make any effort whatsoever to disseminate their no-reference policy to employees, it's just a CYA measure they adopt if communication happens through channels they're directly accountable for)