Relationship between precession and dating ancient alignments Perusing the topics here. I am convinced that this is the right place to get some answers. Although it does appear that my question should be relegated to the "childrens table".

I am curious to understand more about the topic in archeoastronomy that is used to date ancient alignments utilizing calculations based on precession (which I very basically understand as an imaginary circle drawn in space by the earth's axis-line as the earth wobbles).

For example a "temple" in Peru has been dated as being aligned with the summer SOLSTICE(es)[edited] as of 6000 years ago by unnamed experts in the field. Other unnamed experts date it at 28000 years old - to which the first set of "experts" grudgingly concede is "remotely" possible - with an absolute qualification that there was no one here to build it that far back.(Statements of absolute certainty like this and, without proof make me itchy)

First part of question is: Why the huge discrepancy in the dating? Isn't the concept of precession a proven, quantifiable fact? (OK, that was two questions.)

Second part of question is: How do the first set of experts find themselves entrenched in their dating if they must also grudgingly agree that the second dating is remotely possible? (Both groups agree that neither the Inca nor any known predecessors actually built it.)

Anything which can help me to come to grips with this dating rationale would be great.

I am not versed in astronomy whatsoever. I can barely find Sirius on a clear night. And, math is also a foreign concept as well. 
What I DO understand is Ancient Civilizations. 
So, I would like to understand this topic more so that I can discuss it with others in the field - without sounding like a complete idiot.

[Edit to clarify before more protests stack up] I acknowledge that I did not recall and therefore omitted the fact that non-solar stellar alignments AT THE TIME of summer solstice are the basis for this alignment-dating. At least that is the theory I am discussing. (There are others) One window frames the Sun at sunrise while another frames some star. The third window... I cannot locate a theory of what it was supposed to be for. I just wanted to understand the basis for DRIFT over time. And, the accepted answer does that very nicely. Thank you everyone
The answer is fairly simple.   It takes about 22,000 years for the Earth to perform 1 spin or move 360 degrees along it's axial precession.   The 22,000 year cycle means that the temple was lined up at 6,000 years ago and at 28,000 years ago, as well as 50,000 and 72,000.

In other words, if we build a statue that points directly at the North Star, In a couple thousand years it will visibly no longer be pointing at the North star, but in 22,000 years, after a full circle, it will be pointing at the North star again.   More specifically the North Star will apparently move in a circle that takes 22,000 years to complete, moving away from and back towards the celestial north pole.

Any skepticism on the 28,000 year date wouldn't have anything to do with alignment as the alignment works just as well with either date, and it works for any period a full circle in the past, like 50,000 years ago.  The skepticism is likely related to doubt that it's that old.   

Similar to the hour hand on a clock that takes 12 hours for the hour hand to return to where it started, the Earth takes about 22,000 years to return to the direction the North Pole is pointing.   That means, no time between 6,000 and 28,000 years ago will line up.  Those are the two most recent alignment periods.   It moves in a circle in 3D, more like the picture below than like a clock.



As an astronomical note, I want to point out that 22,000 is somewhat inaccurate.   The Earth's axial precession in and of itself is about 25,771 years, but that's only part of the movement.  There's also a larger, slower apsidal precession which adds to or subtracts from the 25,771 year wobble.   These together affect the alignment of the Earth to the mostly fixed stars, and that period varies, but it was about 22,000 years between 6,000 and 28,000 years ago.   It can take as little as 20,800 years or as many as 29,000.   Average is about 23,000.

Many Native American structures lined up quite well to astronomical alignments, so dating ancient structures by measuring when it lined up a reasonable approach.    As a related, somewhat similar example, the Mayan 2012 prophecy is also based on an astronomical alignment and they were, as I recall, a year or two late, but it was still a very good estimate given when they made it.   Understanding these alignments requires seeing things in 3 dimensions and that can be a little confusing to try to picture.