This—the ability to audit what's running on the backend you're talking to—is in large part what people get out of smart contracts on e.g. Ethereum. You can take the contract source code from GitHub, compile it (deterministically), and validate that the deployed-on-chain smart-contract binary is the same. The blockchain nature of the platform then ensures that the contract will do exactly and only what you "expect" it to do (i.e. it'll do the same thing "in production" that it does when you test it on your own machine, since any node that tries to execute the code differently would diverge its state from the consensus, and be ignored.)

In essence, a Turing-complete smart-contract blockchain is a deterministically-trustworthy compute-hosting service. It's one that has the disadvantage of all the overhead distributed auditability requires; but at least has the advantage (compared to centralized compute-hosting with remote-attestation) that it already exists and is usable right now for real-world use-cases.

(And you can also reduce the blockchain-y overhead by moving whatever backend business logic you can out of the "trust kernel" into untrusted regular machines, and then just having the "trust kernel" do the important stuff. CryptoKitties is a good example of this: the only thing their smart contract does is track who owns what kitty, because that's what people would try to dispute by forging transactions. The rest of the stuff is state in a regular centralized RDBMS, because it's dictated by the service, rather than by user input, and so is not under dispute.)