Yes, you are missing something important in the second sentence 「よく道を聞いてもらいます。」. Your understanding of the first is good, judging from the TL.
The second sentence, by the way, is 100% grammatical but its content/meaning is more than just weird. It is highly unlikely that a policeman would say it unless there was an incredibly super-shy policeman somewhere.
「よく道を聞いてもらいます。」 = "I often have people ask others for directions FOR me."
This means that the cop not only often gets lost but he also chooses to ask people around to ask others for directions instead of asking them himself when he gets lost. Thus, I called it more than weird.
(I must mention that in highly colloquial speech, the second sentence with 「聞いてもらいます」 is actually used occasionally by a small group of native speakers to mean the virtually same thing as 「聞かれます」. That is, however, a substandard usage and it would be unlikely that your professor would have meant to introduce it in class.)
やる/あげる/もらう/くれる are very important key words (and that is just an understatement). One will not be able to speak or write natural Japanese without being able to use those correctly because with no exaggeration, we use them all day every day.
「～～てもらう」 implies that the person in question is the receiver of a favor or service. In the sentence 「よく道を聞いてもらいます。」, that person is the speaker who is a cop.