To see how/right wrong it is, you can actually look at the primary source material and see for yourself.

Here for example is an image of a pre Julian calendar http://en.wikipedia.org/wiki/File:Roman-calendar.png

Among other things, you can also see another bizarre truth: the pre Julian calendar did not have a leap day, it had a leap month (more or less randomly inserted sometimes to delay elections). It's labeled INTER on the image.

The terms NON and EIDVS are the Nones and Ides of each month the latter of which I imagine Julius would have liked to reform out of the calendar all together. Hindsight.

Which reminds me of a not so useful poem:

In March, July, October, May,

The Ides are on the fifteenth day,

The Nones the seventh; but all besides

Have two days less for Nones and Ides.