I’m also having this same issue. Twitter Cards were previously working fine for me until after I went on a PCI Compliance binge and blocked all weak ciphers. Now when I try to validate a card, I just get the same SSL Error message that everyone here is reporting.
Can you Twitter people provide any guidance with a list of ciphers that are supported? I know your documentation says to use RC4, but that’s a PCI Compliance forbidden Cipher.