[Justa]

Try adjusting a little to the left or right. The tail is clearly visible to me. The top is on the left, rudder and markings on top, it's 'forward' being down. Imo this is no reflection or artifact. It is also visible as a seperate object when zoomed out towards the end of the clip.

[Alberta's Child]

At the speed at which that shuttle was traveling, there would have been no details visible at all even from a high-powered lens. Even a normal re-entry involves a lot of intense heat due to friction between the shuttle and the atmosphere.