Thanks to Dave Chen's suggestions, I realized I must have misplaced my certificate. The problem is solved by this certificate which is provided by the cURL creator (extracted from Mozilla): https://curl.haxx.se/ca/cacert.pem
So after downloading this cacert.pem file into your project, in PHP you can now do this:
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, TRUE);
curl_setopt($ch, CURLOPT_CAINFO, "/path/to/cacert.pem");
Alternatively, this can be set globally by adding the following to your php.ini
curl.cainfo=/path/to/cacert.pem
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