Haven't watched the videos (no time atm) so I don't know if they address this, but the mayans' belief in a cycle of death and rebirth is not in any way linked to the calendar archaeologists found. Dec. 21, 2012, just happens to be when that calendar runs out of dates. To put this in familiar terms, we don't freak out that the world is ending every New Year's Eve, we just get a new calendar.
To further debunk the myth of the 'mayan apocalypse' happening soon, archaeologists have uncovered at least one other mayan calendar with dates past Dec. 21, 2012. Also, modern day mayans (they still exist, it's just the civilization that collapsed) don't think the world will end on Dec. 21 either. People be crazy.
Unrelated, I'm part mayan, which is why I've actually put a little time into looking these things up (slightly interested in my heritage). I don't think the world's going to end, so neither should you =)