The simple answer to this is: the NAS.
The disk is in the NAS. Only the NAS can ever write to the disk.
The less simple answer to this is: both devices are involved in the process of writing content to files - and a malfunction in either device could cause a problem with the content.
The less simple still answer is: if you use the SMB protocol to expose a disk then you are exposing only the file system, not the underlying disk. So it should be impossible for the client device to corrupt the file system - but the client device can corrupt content, move files, delete files, create files.
If NTP is disabled and the time were ridiculously wrong and you had software on the NAS archiving unused files, or you were doing backup and restore operations or copy operations that were sensitive to the time, then it might matter. For normal operations, the time shouldn't matter, other than meaning that the time that would show on files would be wrong, which would be annoying.
Even with NTP disabled, some devices that offer a web interface allow the web browser to synch the device’s time with the time on the client.
Is the time on the client actually wrong? Badly wrong?
What kind of "network errors"?
If you mean “your network is corrupting data in transmission” then
a) some level of corruption of data in transmission will be detected, even corrected by retransmission
b) TCP is not massively robust - and so if your network is really bad and the files are really large, you run the risk of undetected errors (for large files it is recommended to run a cryptographically strong hashing algorithm over the file at both ends and confirm that the hashes are equal) - of course higher level protocols may add their own error detection
But “network errors” could mean many things?