Indeed. To the topicstarter it may be remarked, as a "pons asinorum", that a great many compounded verbs (wherewith I refer to contractions of particles with verbs), such as "con-venire", "in-haerere", etc., are used with the dative of the indirect object. Therefore, when you see such a word and a dative in the same sentence, the dative, as Ulpianus correctly observed, is often of the indirect object. Notice moreover, that said verbs may also occur, not with the dative, but with the (repated) preposition that is already attached to the word.
There is generally a difference in meaning, in that the dative appears to signify more of a metaphorical relation (for instance in this sentence upon which I, fortuitously, stumbled yesterday): "(Ipse Pompeius, ab inimicis Caesaris incitatus, et quod neminem dignitate secum exaequari volebat, totum se ab eius amicitia averterat et cum communibus inimicis in gratiam redierat), quorum ipse maximam partem illo affinitatis tempore iniunxerat Caesari" (B. C.), whereas the preposition+case conveys a litteral meaning, such as in "morbi inhaerent in visceribus". The difference seems apparent: in the first sentence Caesar isn't writing that "Pompeius litterally fastened, with a rope eg, the greatest part of his enemies to him (sc. Caesar)". Yet in the second sentece the literal meaning is employed: the writes does consider that ills de facto cling to the internal organs.
I'd like to make a further remark to benissimus. Although I agree with his analysis, I disagree with his rendering of the meaning of "quaerebant". I don't think "quaerere" means "to ask" here, but rather "to seek (to acquire)". Thus, the sentence as a whole seems best to be translated in the following manner: "Originally gladiatorial battles used to be organised (to take place) during the funeral procession, but later the candidates for the magistrate employed such spectacles to acquire the votes of the people"