"how could he prove that his ideas were better?"
Because he tried it on himself (except for multipacing methohd because Frank Howell wasn't doing it at the time) on more than 10 years of trial and error and it worked best; and his runners started winning Olympics and setting world records when he applied it on them as well.
You have to remember; with the Lydiard system, results came before theory. And also; I noticed someone starting to "generalize" things (on the Lydiardism at least) wrong way again--Lydiard's conditioning was never done at single-paced jogging or LSD. There are different paces and efforts and, as one guy said (brilliantly, I might add), quite often run over very hilly courses. He just preprared himself and others to run fast before they actually go out and run fast. That's a logical way to train at least to me; why run before you can walk?
Frankly, also, I really don't think Arthur would have opposed to multi-paced 80mpw IF they are done in a correct manner. What are we trying to achieve by introducing "multi-paces"? Just so you can get the mechanics at faster pace--or closer to race pace--going? And also I don't think he'd opposed to tempo runs or long intervals, or even short intervals if done correctly, during conditioning either. Comments like that would quickly lead to the myths of "Lydiard is nothing but one slow pace" or "Lydiard never does tempo or interval".