This is true, but nevertheless you cannot place your trust only in the manufacturer of the SSD/HDD, as I have seen enough cases when the SSD/HDD reports no errors, but nonetheless it returns corrupted data.

For any important data you should have your own file hashes, for corruption detection, and you should add some form of redundancy for file repair, either with a specialized tool or simply by duplicating the file on separate storage media.

A database with file hashes can also serve other purposes than corruption detection, e.g. it can be used to find duplicate data without physically accessing the archival storage media.

Verifying at higher layers can be ok (it's still not ideal!), but trying to actively fix things below that are broken usually quickly becomes a nightmare.