The answer is that the shita is correct, but they picked the wrong rebbe. That’s all. How should they have known he was the wrong rebbe? Not from any one incident, but over time they could have realized that something is very wrong.
One warning should have been if the reports are true that they were discouraged from learning chumash, mishnayos, gemora, rishonim, shulchon oruch, etc. NO legitimate rebbe or system does that. And no, Neville Chamberlain, Lubavitch does not do that. Lubavitchers learn nigleh just like everyone else. Certain post-acharonim may be discouraged, but nobody before ca 1800. On the contrary, Lubavitch tradition is that all the commonly accepted seforim before the Shach and the Taz were written with ruach hakodesh.