He also claimed that Apocalypto was an incredibly honest, authentic, and accurate portrayal of his civilization, which is something that I knew wasn't true when he said it. I bring this up because, frankly, I kind of doubted everything he said following this.
Your guide’s statement would have been subjective at best, and also probably misleading unless he qualified the statement. The first thing to note is that there were 3 calendars used by the Mayans, not just one. The most well known Mayan calendar had 260 days and was thus not a solar calendar like our own. If your guide wants to call it perfect and the most accurate, he can, but it wasn’t used to track the solar year like we normally think of as a primary purpose for a calendar.
The Mayans also did have an understanding of the solar year, including the acknowledgment that the year was closer to 365.25 days instead of 365 (the reason we have a leap year), which consisted of 18 20 day months plus 5 days at the end of each year to supplement and which were generally considered to be a time of bad luck.
Finally, the third calendar system was called the long count, which marked the days since a mythological starting point thousands of years before the Maya civilization and helped keep track of longer periods that had passed. Ultimately the Maya used a combination of multiple calendars to mark specific dates, so it was a more complex system in that sense but not necessarily better or more accurate than modern calendars except for their religious purposes.