That's a fair point. It just doesn't seem obvious in that particular video. If the main factor in visibility were the angle from which the plume is viewed, one might expect to see a continuous change in visibility of the plume as the angle changes. But at 0:11 in the video, when the planes are viewed at roughly a half-turned position, the plumes are already hardly visible behind the nozzles.That's because the plume is 10 times thinner when viewed from the side compared to viewing it directly from the back, see figure in post 315 above. A 10x thicker layer of hot gases is much more visible.
However, that is just one video, and others, like this one, show a variety of effects:
For example, at 1:02 the plane (a BAe Typhoon) shows a narrow concentrated plume projecting behind the nozzles and gradually blending into the air behind, while at 1:13 the same plane shows a huge flaring plume extending much further back; then at 1:20 another plane (an F18) also shows a large plume. I don't know how far these differences are due to characteristics of the engines or fuel (e.g. the use of after-burners), or to the optics of the cameras.
So far as glare is concerned, the optics definitely come into it, as glare by definition is the appearance of light (in this case IR) spreading beyond where it should appear with a perfect lens, sensor, etc.