What Gandalf Knew: Book vs Films

Hi Dr. Olsen,

I'm new here and am not sure if this is the right spot, so if not: sorry! Over a few instances of the Exploring LOTR sessions, I recall hearing how the films blundered a bit in Gandalf leaving Frodo and Sam to fend for themselves between the Shire and Bree. I think it comes down to "if Gandalf knew the Nazgul were pursuing him, why did he leave them alone?"

This is the sequence of events as I can recall from the film:
1. The Enemy knew of the name Baggins and Shire. Frodo and Gandalf decide he must "make for the village of Bree".
2. Gandalf is to consult with "the head of [his] Order" who is "both powerful and wise. Trust me Frodo; he'll know what to do."
3. As Gandalf is about to leave Frodo and Sam, he warns them (a) the Enemy has many spies in his service: birds and beasts, and (b) never to put the Ring on for the "agents of the Dark Lord are drawn to its power."

Fast forward to Isengard where Gandalf and Saruman are talking:
4. Saruman mentions that "the hour is later than you think. Sauron's forces are already moving. The Nine have left Minas Morgul..."
5. Gandalf: "The Nine?" (upset)
6. Saruman: "They have been spotted crossing the river Isen on Mid-Summer's Eve disguised as Riders in black..."

Yadda yadda, I am sure you've got it as memorized as I do. So, until that moment, there was no mention of Nazgul, Ring-wraiths, or black riders. Sure, the ENEMY has many spies, and the ENEMY knows the name of Baggins and Shire, but at that time, Gandalf didn't know they were in imminent peril. In fact, as soon as Saruman says this, Gandalf literally turns to leave, when Saruman slams the doors in his face with the Wizard fight ensuing.

I think what has happened is that the visuals of the Black Riders were intercut into these dialogue scenes, so we are aware of them, but the characters did not know they were in pursuit.