I'm a bit confused about the status of indirect objects as described in this lesson (and in the video). To my knowledge of English grammar, in "I speak to Paul", "to Paul" is a prepositional phrase and not a preposition (to) + an indirect object (Paul). Also, as far as I know indirect objects cannot occur without the presence of direct objects.
Can I instead just memorize that you use the pronouns "lui" and "leur" only with verbs that are normally followed by "à"?