Also, just because she can explain 'how' they charted precession by measuring the distance stars traveled with sticks...doesn't mean they did.
Which is the problem with experimental archeology. We can work backward from what we have today and find a way to use relatively primitive technology to form a rough substitute.
And a archeologists preconceptions will likely shape the results, like with the Baghdad Batteries.
As for the people being as intelligent as we are today, you're right, in a way. However, some our intelligence is due to our upbringing.
For example, take someone from tribal Africa and toss them into our world, even with constant work, their mental process would be different.
Compare your thought process to your grandparents. Now multiply the difference by cultures and time.