So, I just hit upon this error while trying to setup a fresh wp 3.7 for a client.
My own blog, on my server running 3.6 is totally fine with it.
And here’s the output of HTTPS Debugger –
[PASS]: Your WordPress install claims to support HTTPS Connections
[PASS]: Checking that the HTTPS Root Certificate bundle exists and is accessible
[PASS]: cURL is installed and supports SSL communication, cURL Details: version_number=466688; age=3; features=49692; ssl_version_number=0; version=7.31.0; host=x86_64-pc-linux-gnu; ssl_version=OpenSSL/1.0.1e; libz_version=1.2.7; protocols=dict,file,ftp,ftps,gopher,http,https,imap,imaps,pop3,pop3s,rtsp,smtp,smtps,telnet,tftp
[PASS]: OpenSSL is installed. OpenSSL 1.0.1e 11 Feb 2013 268439647
[PASS]: Checking if stream_socket_client exists
[PASS]: Checking if openssl_x509_parse exists
[PASS]: Verifying api.www.ads-software.com resolves correctly.
[PASS]: [Streams] Communication with www.ads-software.com suceeded, it took 0.862 seconds
[PASS]: [cURL] Communication with www.ads-software.com suceeded, it took 0.842 seconds
[INFO]: PHP Version: 5.5.4-pl0-gentoo