Jetpack and SSL verify problem

I’m trying to set up Jetpack 1.6.1. When I try to connect to WordPress.com, I get an error:

Jetpack could not contact WordPress.com: register_http_request_failed. This usually means something is incorrectly configured on your web host.

Error reading ca cert file /path/to/file

I’ve tried to sort this out with my hosting provider, but we can’t make it work. They figured out that they can get cURL to work over https by setting the SSL verify option (CURLOPT_SSL_VERIFYPEER) to false.

I tried adding the error message I get to the list of error messages in _wp_remote_request() in jetpack.php, but that doesn’t help. That just replaces the error message with the jetpack_id error message.

Any ideas how to get Jetpack to connect? My hosting provider is helpless here, and I don’t have a clue either.