|Bernard of Botone (d.1266) gloss on Leap Day|
Except it wasn't.
Truth is, it just wasn't that simple. The standard Roman year at the time of Julius was 355 days. A "intercalary month" was added every three years or so to even things out and restore some normalcy to the spacing of festivals. The new year started on 1 March, and so the "extra month," which was called Mercedonius, was inserted prior to 1 March.
But that would throw things off even more—adding that month made those years 377-8 days long. So that the year would not get too long, they shortened February to just a little over three weeks. A year that needed Mercedonius had a February that ended on the 23rd. Why the 23rd? because that was Terminalia, the festival of Terminus, god of boundaries, and therefore a fitting end to the month.
Julius realized that this was a mess of overcorrecting for the astronomical inequality, and so he demanded that his scholars figure out what the calendar needed. They shifted some months, rewarded him for his wisdom by naming the seventh month after him, and told him the calendar could be kept stable by adding a single day every 4th year.
But where to add it?
Well, since inserting a correction in February was already a common practice, why not there? Excellent! So it was added—right after the day after Terminalia. There was no interest, however, in giving this new day its own identity—after all, it was only going to be around every four years, so who would count on it? Therefore, instead of calling it 24 February, they called it bis septum [Latin: "twice sixth"] because 24 February would have been the sixth day before the Kalends of March, so they would simply have 24th February repeated.
Therefore, even after the Leap Day was introduced into February, there was no 29 February until the Middle Ages, with the widespread European adoption of a sequential system of numbering, rather than counting forward and backward from the Ides and Kalends of the Roman system.