I entirely agree with Calpurnia that the 'complications' may be over-elaborate in this case, and, with the exception of one point (see below) with her scholarly article on the subject.

According to Cassius Dio, JC was born on the day of the ludi Apollinares. This was a.d. III Idus Quintiles, the thirteenth day of July, which date was established in 208 BC (there is a mistake, I am assured, in Livy XXVII. 23, where he suggests the festival was on the third day before the Nones). However one converts the day to conform with subsequent adjustments to the calendar, the third day before the Ides of July is still 13 July. Otherwise, if I understand the purpose of the conversion tables, we should be celebrating New Year's Day on a different date each year!

Calpurnia suggests, however, that JC's reform of the calendar was undertaken in his capacity of Pontifex Maximus. Zwi Yavetz, in "Julius Caesar and his Public Image" (1983) suggests that it was done in his capacity as dictator, since as such he could issue 'edicta', but as Pontifex Maximus he could only provide for intercalation. In short, Yavetz sees the reforms as a political exercise, and, knowing JC as we do on this channel, this seems a plausible explanation.