Hey look: They are actually called tonsils! I thought he was just comparing them to my tonsils (which are always enlarged, and an apt comparison). But when I talked to him again yesterday, he said it again, so I decided to look it up.
He thinks that there's a possibility of Chiari Malformation, which has a high CFIDS/ME & FM comorbidity rate:
The best known of these conditions is the Chiari malformation, in which the cerebellar "tonsils" (a portion of the cerebellum, shaped like the tonsils in the neck) extend several millimeters through the opening in the base of the skull (the foramen magnum) that allows the spinal cord to attach to the brain. This puts pressure on the brain stem and spinal cord. In a less well recognized but perhaps much more common condition known as cervical stenosis, the spinal canal appears normal but is actually too narrow for the spinal cord. Sometimes a condition called syringomyelia develops, in which a cyst grows in the spinal canal, putting greater pressure on the spinal cord.
Yeah, I don't especially like the sound of any of those things, or the treatments (which say things like, gee, I don't know - brain or skull surgery), but ain't gonna worry about any of that until I have to. Got an EEG this week, the neurologist the week after. I will definitely keep you posted!