I beg the differ.
If I place a signed message in the Bitcoin chain, can you then modify that message?
If you can prove that you can somehow modify the message, I'll give you $1,000,000 USD tomorrow.
It makes no sense to say that the blockchain is tamper proof because the blockchain is just information. Tamper "proofness"/resistance is first a property of the devices storing the information - once you get into custody chains, provenance documents, etc. that's when a system becomes tamper resistant. At best the blockchain as a system is "tamper evident" in the colloquial sense because the network of all the other nodes decides which bits of information form the "real" blockchain. However, without verifying the (physical) identity and data integrity of the devices that run (at least?) 50%+1 of the nodes, you have no idea whether the system has been tampered with.
But that's just a question of scale - if you have a rando-blockchain you use for immutability internally then how trivial would it be for me to spin up five servers to outhash you and rewrite history?
I think that's an unrealistic requirement. There's tamper-evident and tamper-resistant but AFAIK nothing is tamper proof. Best you can do is an HSM with a tamper resistant HMAC with keys and a running checksum in unrecoverable ROM coupled to the packaging.