Or they could just implement trusted timestamping (RFC 3161). Using a blockchain is a heavy-weight solution and is rarely the right one.
https://en.wikipedia.org/wiki/Trusted_timestamping#Trusted_(...
You really need better auditing than that, which is why the certificate authority infrastructure now relies on a blockchain - Certificate Transparency - for auditing. Similarly, for timestamping specifically, Guardtime has used a blockchain for auditing their timestamps since well before blockchains got called blockchains.