The Cobra guy indicated he was having tranny problems (bad 2nd gear synchro). Hard to say how much that would cost him time wise in a short run (up to around 60mph for 1st and 2nd gear), but likely enough that the story is entirely believable.
If the Cobra had the vertical "jewel" taillight sections, it was rated at 305 HP with the modular 4.6 (1996-1998?). If it had regular horizontal taillight sections, it was rated at 240 HP with the 5.0 (1994-1995?). I'm not entirely sure on the years, but the cars look very similar except for the taillights. I'm sure a Ford owner can correct me (GM guy myself) on any of the details that need clarification.