AES 5-round Square attack, how to choose plaintexts?
In statistical attacks (such as square), if we can reduce the key space, it will be considered successful. Here, as you pointed, there are false-positives and they should be considered as correct key candidates. But the point is that the distinguisher has removed some incorrect keys and has reduced the key search space. After finding candidates for the correct key, you should do exhaustive search among them or try other attacks to even reduce the key space further!
Here, choosing the plaintexts does not have that much effect on the false positive, since different keys will change the chosen set differently.