--snip--
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.
He never say the private key is hold/accessible by the carrier though. There are different ways to do that such as
1. Storing the private key using built-in SIM card storage[[1].
2. Generate and store the private key using built-in secure element on the SIM card[2].
[1]
https://www.techwalla.com/articles/sim-card-storage-capacity[2]
https://www.tomshardware.com/news/host-card-emulation-secure-element,28804.html