"I even know of organizations where design and development of the testing environment begins at the same time as — or even well before — application development."
This is personally how I approach nearly each piece of software I write (whether it be Perl, Python, C, C# etc), and most of my code has 98%+ coverage (with coverage being covered in dozens if not hundreds of different angles).
That said, the vast majority of companies I've worked for or contracted for don't take this approach as it's too costly. Businesses need to get product out the door, so proper Test Driven Development (TDD) adds a massive delay to realizing Return on Investment so it's mostly eschewed for develop it now, hope it works, but if we have to fix a bug later, THEN add tests for that one piece.
It's a sad reality that profits outweigh quality, but that is the world we live in, unfortunately.
Now, if you know of a specific shop that does use TDD by default, please let me know who :)