signing the document is same as Signing the hash wrt to providing same level of data integrity

Signing a document directly and signing its hash both provide the same level of data integrity protection because the signature operation mathematically operates on the hash in both cases. When you 'sign a document', the actual cryptographic operation first hashes the document then signs the hash. Explicitly hashing first just makes this process explicit. The security guarantee is identical because any change to the document changes the hash, which invalidates the signature.