> relies on you trusting the client to send you true information about data

ZKP's are not magic, you need a cryptographic operation on which to operate the ZKP. this way you can conceal the input while still proving something about it. this works because the ZKP follows the trace of execution through the cryptographic primitive which proves it was executed properly and then the output was validated by some public measure.

conversely, if ZKP's ever get fast enough to be useful for this you can prove a public input (ex. source code) was compiled properly into a public output (ex. binary). for obvious reasons doing this only makes sense when it's efficient otherwise you can just execute it yourself.