How isolated are different areas of the brain?
Well, to answer your question, both your hypothesis are true, at least partially true.

The brain has several known specialized connections called neural pathways that connect specific areas of the brain and are responsible for determined functions.

For instance, when you move your leg, the stimulus starts at the motor cortex and travels through the pyramidal tract to your leg and then back.

However, one can argue that the stimulus didn't start at the motor cortex. Why? you thought about moving, then made the decision and only then perform the real action of moving your leg.

And here's a more complex (and maybe humorous) example:


You see a dog running ferociously at you. 
The stimulus travels through your visual pathway to your visual cortex. 
The image of a dog forms in your brain. 
It then travels to your Hippocampus. 
You realise that's a dog and also remember a traumatic childhood experience with a dog.
The stimulus travels to your amigdala.
You feel fear
The stimulus activates the sympathetic system.
You're now prepared to fight or flight
The frontal lobe is activated
You decide to kick the dog
The stimulus goes from your motor cortex to your cerebellum
Your cerebellum "remembers" the karate classes you had as a kid
The stimulus goes to your leg
You kick the poor dog. He runs.
Nucleus accumbens is activated
You feel good with yourself


So, in short, the brain has pathways that connect specific areas of the brain but, in a sense, all parts of the brain are connected either directly or indirectly. Like the saying "all roads lead to rome!" 



DISCLAIMER: I do not endorse animal cruelty.