Or a bullet that had tumbled 180 degrees.

Royell has hit the nail on the head about your Looney Tunes grasp of reality.
You are clearly unaware that you are suggesting the bullet tumbled 180 degrees, straightened up while it passed through his jacket, then resumed a-tumbling.
It is physically impossible for a bullet rotating at such an incredible speed to make such a small hole in his jacket.
In your cartoonish view of the world the bullet exits JBC's chest backwards.
It must then tumble a further 360 degrees in order to enter his wrist (and leg) backwards.
The distance it has to travel is around 12 inches/1 foot.
Let's say the bullet exiting Connally's chest is travelling around 1000 feet per second [Sturdivan estimated "somewhere between 1,100 and 1,300 feet per second, roughly."]
This means the bullet is spinning 1000 times per second!!!
1] Where does this incredible rotational energy come from?
2] How can a 3 cm object spinning 1000 times per second leave such a small hole?
3] What nonsense are you going to come up with next?