Thinking about this more, like every blockchain, this only makes sense if there is an incentive to publish each log entry as quickly as possible. Once it's published, of course it's tamper-proof, including against "the operator of a recorder can delete the bad day". Presumably the incentive to publish and the protection against the operator choosing to "never write a record at all" is the same: You must get paid for publishing a log entry. Because a log entry is, quite literally, "proof of work".

But if you're incentivized to publish as quickly as possible, then your customer gets the log immediately, and there is no need for a "trusted" third party to act as a "witness" and seek rents for not doing anything useful.

And none of the above protects against the vendor using your sensitive data to (a) do the work as contracted, with a cryptographically verified log and everything, but also (b) copy/analyze/abuse said data without telling you.

It's 2017 again, and someone on HN is inventing "blockchain for X", poorly. (Also note that it doesn't matter what kind of work X is, except for aligning this with HN's current main interest.)