Take this code:
using System;
namespace OddThrow
{
class Program
{
static void Main(string[] args)
{
try
{
The standard's statements about the order of execution are correct, and not inconsistent with what you are observing. The "Unhandled exception" message is allowed to appear at any point in the process, because it is just a message from the CLR, not actually an exception handler itself. The rules about order of execution only apply to code being executed inside the CLR, not to what the CLR itself does.
What you've actually done is expose an implementation detail, which is that unhandled exceptions are recognised by looking at a stack of which try{} blocks we are inside, rather than by actually exploring all the way to the root. Exceptions may or may not be handled by looking at this stack, but unhandled exceptions are recognised this way.
As you may be aware, if you put a top-level try{}catch{} in your main function, then you will see the behaviour you expect: each function's finally will be executed before checking the next frame up for a matching catch{}.