The reason why the amygdalae are in the middle of the brain is because they are not part of the reptilian brain. The amygdalae interact with many areas of the brain and are in the limbic system. They are often referred to being the "fear centre", but they have roles beyond just being a simple threat detector.
Studies have found the amygdalae to be active not just during fear conditioning, but also when learning to link a previously neutral stimulus with a positive experience by
interacting with reward areas of the brain like the ventral striatum, which is in the reptilian brain
playing an important role in forming memories associated with drug use.
being an important region for the consolidation of memories that have any strong emotional component - whether positive or negative.
the amygdalae (Source: Wikipedia)
There are functional differences between the right and left amygdala. In one study, electrical stimulations of the right amygdala induced negative emotions, especially fear and sadness. In contrast, stimulation of the left amygdala was able to induce either pleasant (happiness) or unpleasant (fear, anxiety, sadness) emotions.
For the idea of 3 parts to the brain, this idea was started by American physician and neuroscientist Paul D. MacLean. He originally formulated the triune brain model in the 1960s and propounded it at length in his 1990 book The Triune Brain in Evolution.
The triune brain consists of the reptilian complex (also known as the "reptilian brain"), the paleomammalian complex (limbic system), and the neomammalian complex (neocortex).
The reptilian complex, was the name MacLean gave to the basal ganglia which consists of the dorsal striatum (caudate nucleus and putamen), ventral striatum (nucleus accumbens and olfactory tubercle), globus pallidus, ventral pallidum, substantia nigra, and subthalamic nucleus.
basal ganglia (source: Wikipedia)
The neomammalian complex (neocortex) is a part of the mammalian brain. The neocortex consists of the grey matter, or neuronal cell bodies and unmyelinated fibers, surrounding the deeper white matter (myelinated axons) in the cerebrum.
neocortex - Human brain right dissected lateral view, showing grey matter (the darker outer parts), and white matter (the inner and prominently whiter parts) - source: Wikipedia
The paleomammalian complex (limbic system) consists of olfactory bulbs, hippocampus, hypothalamus, amygdala, anterior thalamic nuclei, fornix, columns of fornix, mammillary body, septum pellucidum, habenular commissure, cingulategyrus, parahippocampal gyrus, limbic cortex, and limbic midbrain areas
the limbic system (source: Wikipedia)