Idid some digging. cURL does not authenticate ssl certificates. WordPress is supposed to fix that with a library to authorise against. Some earlier/older versions of WordPress had an issue with that. Some servers can not use that library, simply because they’re outdated.
If you’re not using the latest version of WordPress, update first. If that doesn’t fix things, talk to your hosting provider about supporting more modern versions of HTTP/HTTPS and SSL. A lot of “current gen” certificates are being phased out this year for higher encrypted ones. Which are not supported on many older servers. So if you don’t sort it out now, you’ll get issues later on.