On the one hand, it is claimed that one should not depend solely on the judgement of people of authority, but rather try to verify their opinions and learn independent thinking. It is claimed that the fact that a person of authority says X does not yet constitute an argument for X.
On the other hand, many times it would seem that the contrary is true. Trying to apply one's own reasoning can lead to preventing from learning; as it would seem that, especially in the first stages of learning, absorbtion of other people's knowlege, rather than questioning it, is a necessity - even if the learner cannot yet prove this knowledge themselves. Also, insisting on proving or understanding each piece of accepted knowledge is practically infeasible.
In some areas, proponing the recourse of authority has been brought up to eleven. In cryptography, for example, it is strongly encouraged to only use tools brought by experts. This general prohibition of doing virtually anything on one's own seems even more harsh than the usual recourse to authority, which only prohibits doing what experts explicitly discourage. (source: see eight numbered links in the top of this question).
It would seem that statements really are much more likely to be true just because an expert said them, as opposed to statements said by the ignorant - and this seems precisely what argument from authority fallacy disclaims.