I'm not sure that's true. Of course some some details might have been purposefully (or not) ignored or twisted. While obviously Christian scholars were quite picky on which pagan texts to preserve or not (due to various reasons) there is not a lot reason to believe that generally they did their best to copy them faithfully. Of course we are talking about a highly literate society with a strong tradition of analytical history (which was very unique by pre-medieval standards at least).
> Quite similar to Romulus
The claim that some specific historian might have invented him out of thin air is far fetched and not really substantiated. Much more likely that the legend evolved over many generations and became a mishmash of fact and fiction over hundreds of years before someone actually wrote it down. Based on other similar cases it's highly likely that there were many competing traditions by Livy's time. So yes, he did very likely tried to reconcile them and picked how to synthesize the narrative but it's hard to imagine he could have actually invented it because there were plenty of people and other historians who could have called him out on it.