The way the question you linked to is worded, I don't feel it is proper to say that either a or the is incorrect. The definite article certainly feels more natural to a native speaker, but the indefinite is not incorrect.
Why does the definite article sound better? Because in this case, the road is a class noun (in my opinion). I think the answer here is basically the same as I gave here. In short, one "crosses the road" in the same sense that one "plays the clarinet" or "goes to the beach".
I don't agree that the is used because the young man can only cross a particular road; by that logic, the young man could never be wearing "a hat", because he must be wearing a particular hat.
I also don't think the "pure idiom" argument works, because one certainly can "cross a road". One would use that phrasing if the road itself were important or needed to be emphasized. ("What did you cross?" "A road.") Certainly if the road were being described in some way, one could "cross a two-lane road".
The use of class nouns gives us three levels of specificity, even though we only have two types of article:
1) "Cross the road" as generally used is totally unspecific; this usage is more about the act of crossing than the road itself. This could be absolutely any road.
2) "Cross a road" is still unspecific, but it is referring to a particular road--just one that has not yet been specified in context. Ask a native speaker why the chicken crossed a road and his or her first reaction will be to wonder which road.
3) "Cross the road" in the sense of referring to a particular, specified road is also available. ("I'm on the opposite sidewalk; you need to cross the road to get to me.") However, it is obviously indistinguishable from #1, and the tiny difference in the overall meaning between the two rarely (if ever?) matters.
So here we might argue that the preference of most speakers in most situations for #1 when #2 would work is idiomatic, and maybe there is an element of truth to that--we might say a clarinetist plays "the clarinet", but we wouldn't be likely to say that a constant hat-wearer wears "the hat". However, there is some meaning gained by this phrasing; it serves to deemphasize the road and, as a result, emphasize the act of crossing or the person doing the crossing. If we describe someone "crossing a road", there is a slight sense that the road in question, though unspecified, may matter in some way; describing them as "crossing the road" makes it clear that it does not.