I believe that the Ran had another reason for stating that the inhabitants of the city should recite the Megillah on the fourteenth, which fits in perfectly with the Ran in Pesachim. The Ran in Pesachim begins his answer by stating that we are unsure which two we should be lenient with. Therefore, he says, since we cannot choose, we should do both. He adds that we must recline during at least one of them because otherwise this would be mevatel the mitzvah entirely. But he first prefaces that we should attempt to choose which one we should do. He resolves that regarding the four cups of wine they are all equal and therefore we cannot choose.
However, regarding reading the Megillah on the fourteenth or the fifteenth, the fourteenth is the main day to read the Megillah. The halachha is that if one who resides in a city that was walled from the days of Yehoshuah ben Nun reads the Megillah on the fourteenth he has fulfilled his obligation. Therefore, applying the Ran’s logic that in a safek d’Rabanan we first see which one of the two to pick, we now see why the Ran would say that they should read the Megillah on the fourteenth day of Adar.