It's been said that SUR is equivalent to the equation-by-equation OLS:
i. When there are no cross-equation correlations between the error terms.
ii. When each equation contains exactly the same set of regressors.
I would like to confirm whether each condition is necessary or sufficient, namely the second condition. In 4.5.1 Seemingly Unrelated Regression, the author uses an example of SUR with equations that each use the same set of regressors, which seems to violate (ii) if each condition is sufficient.