No, that's not true. Close returns an error only if an IO error (including broken network in case of nfs) has occured after the last write so the kernel couldn't report it sooner.

From close(2):

Not checking the return value of close is a common but nevertheless serious pro- gramming error. It is quite possible that errors on a previous write(2) operation are first reported at the final close. Not checking the return value when closing the file may lead to silent loss of data. This can especially be observed with NFS and disk quotas.