My watch does not display the correct time. The time it has is about two and a half minutes ahead of actual time. Slightly less.
I know this, and since I know this I can tell the correct time fairly accurately. If I were to reset my watch to the correct time I'd risk forgetting that I reset and assuming it's about two and a half minutes later than it actually is.
Knowing the limitations of your time piece can be valuable It allows one to adjust accordingly. That's how our own system of leap days came to pass. They adjust for the limitations of our calendar which left to its own devices would get well out of whack.
A different method for adjusting would be to just keep track of how out of whack it had gotten and adjust one's behavior accordingly. My watch doesn't really run fast or slow, it's just got the wrong time and so continues to have the wrong time at about the same degree of wrongness as the days go on. I know it's wrong and it doesn't bother me much. It might if I didn't know it was wrong.
If I wanted to, I seldom do, I could figure out exactly how far off my watch was and then, via adjustment, tell the correct time very accurately.
In some people's eyes that makes my watch a very accurate watch. Technically it just has a level of precision and a mostly uniform inaccuracy.
I bring this up in a post with "Mayan Calendar" in the title because of, I suppose, a quote from Silverado: "Life is what you make it. If it doesn't fit, make adjustments."
I adjust for the inaccuracy of my watch. Calendars are forced to adjust for the inaccuracy of Calendars because the solar system never got the message that we'd like to have a calendar that consistently reflected the seasons year after year.
We make adjustments with leap days. Add a day if the year is divisible by four, unless it's divisible by 100, unless it's also divisible by 400 in which case add the day after all.
They Maya people did something more akin to what I do with my watch. The recognized the inaccuracy they took it into account, they learned to live with it. The result was that that their adjustment (which basically involves saying, "If we wait 1508 Haab' years that's the same as 1507 solar years and things line up again") gave them a better approximation of the solar year than ours by a nearly negligible amount.
Presenting that as them having an extremely accurate calendar is like me presenting my watch as extremely accurate because I happen to know how far off it is and can adjust for it.
Their calendar was not accurate. It was wrong. They did an impressive job of figuring out precisely how wrong it was and taking that into account, but the calendar itself was not accurate. The Maya themselves were apparently able to be accurate in their use of it, because they were able to take its creeping inaccuracy into account.