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oops, guess I didn't clarify - if you click through the spaceweather.com link, then scroll down to the 2nd headline (past the comet-as-jellyfish story), they explain how this image happened.
These solar shots are apparently taken as composite images through a telescope (so you're seeing multiple frames, one with the plane silhouetted against the sun, one of the glare from the jet's contrail after it had passed). Originally even the astronomer thought the bright stuff on the RH side was a solar prominence, but then figured out that it was just sunlight shining through the turbulence from the contrail.