Just watched a video on the Sportsman channel showing Melissa Bachman kill a buck with an arrow in the upper leg below just below the chest area!

My! My! My! I wish my bows had that much KILLING POWER!!!

Hip

I have done the same thing, just with a gun. Sever the main artery in the front leg and they will bleed out.

Form a pure wound ballistics science perspective:

A Sharp broadhead tipped arrow it potentially more lethal than a high velocity bullet! Especially when it comes to what view as marginal wounds.

There are a number of reasons for this statement.

If we compare projectile effectiveness we see that the bullet beats the arrow on both counts ie both striking energy and potential to impart energy to the target. However, where the arrow wins is in efficiency ! This is based on its very high Sectional density and thus energy density!
Arrows have relatively low kinetic energy when compared to bullets, but they use this available energy way more efficiently than the bullet.

Because of its extremely high sectional density the arrow induces way less drag than the bullet thus full penetration ( and shoot through ) of the target is often the case.

The concentration of energy by the sharp cutting edge with little drag causes clean "minimal trauma" laceration which in turn reduces venous and arterial contraction. This is the same as our modern "atraumatic hypodermic injection needles "

These injuries when lacerating veins or arteries tend to bleed freely without induction the body's normal vasoconstricting reflexes.

Also:

The total "effective wound volume" of the arrow is very high. There is very little temporary wound cavitation with arrows and high permanent cavitation whereas bullets tend to have small permanent cavities and large temporary cavities ( as per the correct definition of both )

The limitation of the arrow however is its effective range.

The point I'm trying to make is that a "CELEBRITY TV hunting makes an extremely bad shot and still recovers her deer! Back up rifle perhaps? A SHAM?
Who knows?

Hip

Maybe a sham, maybe not. If she had leg shot it with a 300 weatherby, she would have had to shoot it again. Let it go. There’s bigger things to worry about.