I think the White book is wrong in not saying when this applies. Since I am currently re-writing the White book, I shall make sure this appears in the next one!
If you can re-score the board - which is another way of saying do what Ed suggests - then that is definitely best.
What is contained in the White book has two applications.
First, if you are too late to re-score the board, and especially when it is too complicated, for example you have 150 tables and want to make a small adjustment, perhaps because of an appeal, some hours later, this applies.
Second, very little software has yet been written to allow for weighted scores. So if you have a weighted score then you have to do something. Now, if you are running a six table event in your club, you could score it properly, by producing different scores for each table dependent on the various scores, and then applying the weighting to every pair. Even for six tables that is very complicated: for any more it is impractical.
So the EBU method is a practical and fairly accurate method of working out how to deal with scores when you are putting in a manual adjustment, either because it is too late to re-score, or because it is a weighted score.