That's "tamper proof" in the colloquial sense. As a term of art, it means something very specific. For example, see FIPS 140-2/3 [1]

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.

[1] https://en.wikipedia.org/wiki/FIPS_140

If you want to raise the bet to a few billion dollars I'll happily take you on.

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?

Not after you post it, but by infecting your device before you make that message, and tampering when you place it in the Bitcoin chain

So you agree, once it's on the blockchain, it's tamper-proof?