How are anti-counterfeiting efforts done today?

Accounting.

For this use case, think of blockchains as a shared ledger.

If you already trust the accountant, he can set up a conventional database, and you can look stuff up there. Much simpler and cheaper.

A blockchain-based shared ledger is only useful in case the participants don't trust each other. In which case you cannot do anything with it to help detecting counterfeits.

Or when you have a supply chain composed of various participants.

And now you're trusting each participant to enter their portion of the ledger accurately.

The original articles goes into this very problem. What's to stop your mango provider from spraying pesticides all over their mangoes and then entering "organic" into the ledger?

Yup. Turtles all the way down.

I'm not saying blockchains are a cure all. I'm saying I'm keenly interested in using shared ledgers for this use case.

My experiences with election integrity, for better or worse, inform my views (optimism). There was a lot of interest in auditing elections. And it was studied extensively.

For my part, I read up on Medicare fraud and forensic accounting, because they seemed to be the most mature related domains (at the time). My conclusion was that reducing fraud is best accomplished thru simplifying the accounting.

You still need relationships and face-to-face and "trust but verify".

My ultimate hope is that something like blockchains (not talking cryptocurrency, bitcoin, PoW) will somehow make the chasm between the physical and digital worlds smaller. Thereby reducing transaction costs, waste, fraud, uncertainty and so forth.