It's the cryptocurrency that keeps it tamper proof.

Any blockchain can be altered they aren't immutable by nature.

What keeps it immutable is the incentive provided and to not cheat so you can get that incentive.

The whole thing is trustless and everyone is working together aligned on the incentive.

If it doesn't cost resources to secure the chain (which get recouped by the reward) anyone could just spin up a bazillion nodes and take control of the chain and alter the records. And anyone could collide to do so with others to benefit themselves by altering it if they aren't risking a reward, or in PoS, their stake.

If it's a small private blockchain to just keep track of data, people could collude and alter it and it could just be a write only dB with a few admins

What Satoshi did, was invent a way to make a digital item immutable, that was the invention. There were no immutable digital items prior to that. A blockchain isn't just immutable because it's a blockchain.