That sounds pretty dodgy. Omnipay uses Guzzle to make the HTTPS requests to PayPal, and Guzzle bundles the latest root SSL certificates for you. So you should not see any HTTPS warnings.
Does this work locally for you? Have you tried different servers? If you are on shared hosting it is possible that your web host is trying to proxy your requests, which means they are essentially performing a man in the middle attack, potentially making your website insecure.
EDIT: Just noticed that error is actually coming from Buzz, not Guzzle. How did you install that? What does your composer.json file look like? Which version of Omnipay are you running? If you upgrade to the latest version of Omnipay (2.0) it will use Guzzle internally and this should fix the SSL error.