Then you would have expected the missile to target one of the engines and not the fuselage.
Depends on the missile; older MANPADs, which would have trouble reaching 16,000 ft, were designed to hone in on the largest IR signature, typically the engines, after-burner, etc. First generation weapons of that type (SA-7, Redeye) were strictly tail chase weapons; the target had to be moving away from the gunner to present the largest possible IR return.
Newer MANPADs (Stinger, Russian SA-16/18/24) use a cooled seeker that gives them greater discrimination. That allows them to lock on to smaller IR returns, such as the heat along the leading edge of a wing, hot spots on the fuselage, etc. Some of these weapons can actually scan in two different frequency ranges and the gunner can select the best target. These are the same weapons with the ability to reach higher altitude targets, up to 23K.