Question

Why does reflex action not depend on the thinking tissue in the brain

Answer 1

This is because the reflex action requires a quick response that would be slowed down by the thinking process.
The stimulus sends a signal to the receptor and the receptor to a motor and the motor to the effector that produces a response.
This unconscious response is automatic and depends on the spinal cord rather than the brain. This helps the organism in adaptation and escape, in time, to dangerous stimuli that would otherwise cause harm or severe discomfort to the organism.