Do the anchor nav links "know" to smooth-scroll down to appropriate section if the section is an id with the same name?
Yes.
Is that how it makes the association between the two elements?
The '#Link' part in the href attribute will link with the 'Link' id of an element.
It's just that the tutorial markup shows no further code next to the section, and that one works - where mine does not, yet.
If yours does not work then you have an error in your code.
I had div classes for each segment as you scroll down the page because each has unique design properties. Is it OK to simply wrap <section> tags around what were the original div containers to make it a bit more HTML 5 compliant? - Is that a reliable quick fix method, vs. having to re-write?
All of the HTML5 grouping elements, including the div element, are nearly the same; the only difference, apart from the name, is where and how they can be used. See here for more info HTML5 Doctor, helping you implement HTML5 today