So, if I am at a lower prestige DI school and I get the fallback message from a recruit, what does that indicate?  Is this the same as pulling down a DI player to DII?  and if so, how likely does this mean it is the type of player that higher prestige teams will try to pick off from me?

Yes, you can pull the player down just the same way.

You always run the risk of a team with higher prestige going after him. That's really part luck, part judgment call. If you're going after a 4-star player, you can pretty much bet someone will jump you. If you're a DI school going after a 1-star player, you certainly have a chance to hold onto him. (Particularly since you're in a bit of an isolated area -- less local comp.)