Adam, great analysis, and I think you are absolutely right: This one scene reflects the tenor of the entire movie and, indeed, a lot of their movies. Characters may dream. Characters may scheme. But oftentimes, it’s Fate which dictates outcomes. I go into this in my post: The Coen Brothers, Storytelling, and Fate. It features a poem by Ethan called “The Drunken Driver Has The Right Of Way”. If you think of the Drunken Driver as Fate, you can see how that sensibility is innate to their storytelling sensibilities.
Thanks for your observations. They are spot on!