In the book, Freedman states that two assumptions of the standard error of the difference are violated by the way subjects are assigned to control and treatment

In the book, Freedman states that two assumptions of the standard error of the difference are violated by the way subjects are assigned to control and treatment groups in randomized controlled trials (RCTs). The standard error of the difference assumes that a) samples are drawn independently, i.e., with replacement; and b) that the two groups are independent of each other. By samples being drawn, I mean a subject being assigned to a group in a RCT here. If you derive the standard error of the difference, there are two covariance terms that are zero when these assumptions are true. When they're violated, like in RCTs, the covariances are non-zero and should in theory be accounted for. However, Freedman implies that it doesn't actually matter because they effectively cancel each other out, as one inflates the standard error and the other deflates it.