How does block chain guarentee that something going from A to C via B is not tampered with in anyway?

It doesn't guarantee that. As I said, it guarantees that paper trails are permanent and cannot be fudged after the fact.

So you have a permanent paper trail that cannot be changed, what problem has it solved?

The problem of paper trails being changed. When something goes wrong, if you can't trust your paper trail, you can't attribute fault with certainty.

Without an immutable shared database standard, it's difficult for processes like that to cross company lines. And supply chain is a fancy phrase for processes that cross many company lines.

It doesn't ensure that the data is correct, valid, hasn't been tampered with, or even entered.

A supply chain involves 3rd parties who have nothing to gain from this. If the issue is the middle man between A and C, blockchain isn't solving any problem. The distrust is with B, having a blockchained backed paper trail doesn't provide anything a database gives you right now.

You're asking for a single source of truth between A B and C. And saying you cannot trust A B or C, so you want blockchain to solve it, which needs to be created by someone, so you introduce D and now you have a central governing body who dictates everything for A B and C. Or you are A and you say 'hey B and C, you need to use this system we created cos we don't trust you!'.

Blockchain solves nothing in the supply chain.

It ensures that data hasn't been tampered with after initial entry. And that a uniquely attributable digital signature gets recorded at the point of entry, along with a timestamp.

Auditing is a core feature of most modern RDBMS systems.

Anyways the reason why it's immutable is that it's public so everyone knows every transaction. You can just have a normal db and maker it public. Blockchain is overkill in this case.

Also this is a much more niche problem than "supply chains"

No it doesn’t. Private blockchains aren’t immutable. Whoever controls all the nodes can just edit the blockchain however they want.

There's no reason for one actor to control all the nodes.

If I own every single node it doesn’t guarantee that.

If you are the sole person keeping records for a large company in your personal desk drawer, it also doesn't guarantee that.

But nobody designs a process like that.

By “I”, I mean a single company.

Multiple companies could run nodes.

You don't need a blockchain for that, though; just hash chaining or similar.

What distinction are you making between a blockchain and a hash chain? They seem similar.