You may want to try something like:
curl https://api.twitter.com/ -v
instead of the docs page to test. But the command you used works for me too, so it’s probably something wrong with curl or ssl or CA certs.
If you look on the https://dev.twitter.com/rest/reference/get/account/verify_credentials page - there’s a link to a curl command generator under “OAuth Signature Generator”
Make sure your clock is in sync, and your CURL, SSL, NSS (Network Security Services) packages are all up to date on your machine.
