That claim is not supported in the source you linked. In fact, it's directly contradicted several times. For example, toward the end, it quotes the OED:

"The theory that the origin of the phrase [‘beyond the pale’] relates to any of several specific regions, such as the area of Ireland formerly called the Pale … or the Pale of Settlement in Russia … is not supported by the early historical evidence and is likely to be a later rationalization.”

Throughout, your source draws a distinction between the histories of the separate phrases "beyond the pale" and "pale of settlement".

So I guess your statement might be true in the narrow sense that "many believe" the false etymology, just as you can find many who believe that the earth is flat. But that's not a good reason to go around chiding people for using a common expression.