Sounds like a "guess" rather than a "solution". They have noticed a numerical coincidence and formed a hypothesis. Without additional evidence tying the 819-day count to astronomical observations its not particularly convincing.
There's basically no surviving Mayan literature, thanks to the hard work of the Catholic church. So good luck finding more evidence. https://en.wikipedia.org/wiki/Maya_civilization#Writing_and_...
>We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction.
The same individual of whom it's been said
>ninety-nine percent of what we today know of the Mayas, we know as the result either of what Landa has told us in the pages that follow, or have learned in the use and study of what he told.
So yeah, scholarship of the Maya civilization is extraordinarily challenging.