Step 1: Recall how check basin irrigation actually works.
In check basin irrigation the field is divided into small level plots enclosed by low bunds, and each basin is flooded and left to hold standing water until it infiltrates, so the soil and the base of any plant stems inside the basin stay wet or even submerged for an extended period.
Step 2: Test Statement I against that behaviour.
Statement I claims the method suits crops that are sensitive to wet soil conditions around their stems, but the method's defining feature is exactly the opposite, prolonged standing water around the stem, which is why it suits orchard trees and paddy that can tolerate standing water and is avoided for trees whose collar rots if kept wet. So Statement I misdescribes the method and is incorrect.
Step 3: Test Statement II.
Because check basins are simple to construct, need very little levelling precision compared to border or furrow methods, and work well for orchard trees, they are reported in standard irrigation texts as the most widely adopted surface irrigation method across India and many other countries, so Statement II is correct.
Step 4: Combine the findings.
Statement I fails and Statement II holds, giving the combination where the first is wrong and the second is right.
\[ \boxed{Statement (I) is incorrect but Statement (II) is correct.} \]