Talked with the hosting company and we tried to move the site from 5.2.17 PHP server to 5.3 and it broke the site, so we had to roll it back to the 5.2.17 server.
The server team ran the following script:
https://www.hunterbooks.com/tls-test.asp
They said the server supports TLS 1.0, 1.1 and 1.2 and the default preferred is 1.2
I do not know enough about CURL to comment, but they said the script you provided may just check for TLS and if 1.0 or 1.1 exists, the error comes back. Again, i don't know enough to comment, and I don't know what PayPal is looking for when they reject a transaction.
Since the site won't run on anything after 5.2.17, is there anything to fix this?