It might depend on what you mean by "tamper-proof" and what they mean.
One of the benefits of blockchains is the ability to distribute a ledger of data across the entire network. Each node in the network enforces the integrity of the data for the rest.
If you can somehow express your application in a way that can be stored and verified in the ledger (like a hash of the binary), then yes, the blockchain algorithms would simply take care of the rest. Any unrecognised application would be ejected from the network.
If you went the next step so that updates to the apps were enforced by the network, then it is possible for the apps in the network to enforce a certain level of operation so that if one node was altered, then the rest of the apps would revert the altered node.
Those are 2 different types of "tamper-proof". You might need to ask Ethereum what they mean by the phrase.