I'd wager it didn't get muddy immediately upon starting down that road. Once it did, though, it was probably too late with a line of cars behind you and nowhere to go but forward.
You could leave a little earlier.
But, more generally, I agree. It's hard not to follow the GPS and road conditions can change rapidly.
My own anecdote... driving along 495 outside DC, there's a crash on the Woodrow Wilson, and the GPS says "take some side roads" to all 10,000 of us on that stretch of interstate. Massive gridlock ensues, not just on the interstate, but also all the surrounding neighborhood roads as cars tried to pass through parking lots and alleys to get home.
I've faced the same situation but I was alone, and I didn't take the dirt road.
99 cars stuck in the field, 99 stuck cars
turn one round, drive it arround, 98 stuck cars in the field....