Not true. We use the Gregorian calendar which has 365 days + leap days to attempt to measure a single solar cycle. The Mayans used the Mesoamerican Long Count calendar, which measures periods of time much longer than a solar cycle. They didn't need leap days because they didn't concern themselves with measuring individual solar cycles (and putting a crude number of days on it like 365 or 366). Instead, they just use concentric cycles of 1, 20, 360, 7200, and 144000 days recorded in base-20 and base-18. That makes it equally accurate but hard to read for those of us who are used to base-10. For that reason, when talking about dates referenced from other calendars like the long count, we typically convert them to Gregorian or Julian models first so that they're easier to research and understand. That's what happened with the "end of the world" date, which means 12/21/2012 is accurate because it was translated from long count to Gregorian.
Put simply, leap days are irrelevant. The folks who came up with this "end of the world" thing are talking about the point in time that the long count calendar ends. They just told us where this point in time falls on the Gregorian calendar so that it would be easier to understand. It happens to fall on Dec. 21 of this year.
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