Yup, that's how I read it, too. And I think they are quite wrong about it. By the time you're in neutral, the tranny doesn't remember where you came from. Neutral means:
First/reverse gear not meshed,
second speed gear spinning freely on main shaft,
third speed gear spinning freely on main shaft,
input shaft and main shaft not locked to each other.
Now you shift into second, which means you lock the second speed gear to the main shaft. There's only one way to do this, and only one synchronizer to help you.
However, the second speed synchonizer is actuated by a couple of springs. Rather than a worn synchro, it may just be a broken spring.
