"SIM cards as private keys?" This doesn't seem a good innovation where security is of utmost consideration.
No, your SIM card isn't used as private key. Phone number of that SIM card is used to login on their centralized service. But obviously it has different security concern.

It's not used a private key as of yet, but The article says he is looking for a way to use SIM cards as private keys because the current service works against the Bitcoin ethos of not your keys, not your coins.. Personality, I wouldn't trust anything that is controlled by the carrier to hold private keys.