This is FUD. If you run a redundant filesystem like btrfs or ZFS that does checksumming (which you should anyway in a NAS), then ECC memory is only a nice-to-have and not vital.
checksums at the filesystem level does nothing to protect against memory corruption which can overwrite everything on your disk with null values and a matching checksum; fail to write anything to disk and/or do nothing.
But that is the gamble you take every day with every GB of RAM you have.