You folks have the big picture. Supposedly, many years ago an Air Force C-9 (DC-9 -30 series) crashed while departing Scott AFB, about 20 miles east of St. Louis, MO. They supposedly had a fire warning (very loud bell plus red lights) at or just after rotation. The new copilot supposedly grabbed and pulled out a fire handle-the handle which was NOT illuminated! This shut off fuel to the good engine and down they went, having lost or about to lose thrust from the engine with the red light in the handle. That's what I remember having heard.
Because of that accident, Douglas recommmended only flying the plane and cancelling any warnings (d****d loud fire bell!) until a minimum of 800' AGL.
One of our pilots had been flying years for an airline, along with part-time AFRES missions in the four-engine C-141 McChord AFB, Tachoma, WA. During an engine fire on rotation in the simulator, the pilot was given an engine fire. The pilot waited until about 1,000' before he called for the Engine Fire Checklist (whatever the title). He told us that as he watched the red lights go on while he flew to a safe altitude, the excited Stan-Eval/Check Airman (or IP) blurted out "aren't you gonna shut it down?" etc, he told the guy that you don't need to grab anything at low altitude which will shutdown a critical component such as an engine. The "line pilot" was not failed for preventing various hands (3 or 4 crewmembers) from snatching fire handles/fuel control levers until safe coordination could take place.
Sometimes certain elements of US military aviation, with the tense combat mentality, in contrast to airline operations, relied years ago (if not still now) upon quick memorized reflex actions (i.e. reject/abort takeoff for ANY malfunction up to "refusal speed" /V1) in stead of pausing for a few moments, which were meant to be a substitute for experience, but this is not meant to be a sweeping generalization or a critique.