Are you using FireFox? FireFox doesn't use the same SSL root certificates as Windows (e.g. IE). If so, try IE or Chrome instead. I think the issue you are seeing is a certificate chain issue. It would be easy for you to add their certificate to your browsers' root certificates. You wouldn't see the error anymore. However, it isn't easy to know if you are really adding their SSL certificate or a man in the middle certificate. You would need to download the CA's root and chain certificates. Then install those certificates on your device. End users shouldn't be responsible for adding a trusted root store on their devices.
Another issue is they are still allowing some weak protocols (SSLv3, RC4 ciphers). It suggest they may not be very security conscience. I don't use the service, but I don't think I would want them to be responsible for safe guarding my information.
Note: I am assuming Windows is the OP's OS. The same principles apply for other OS's.
