Yes. Because Death is not Instant, even in a clean "apricot" headshot. The human body doesn't just die immediately, even when heart and head are destroyed. Cadaveric Spasms are one problem.
Cadaveric spasm, also known as postmortem spasm, instantaneous rigor, cataleptic rigidity, or instantaneous rigidity, is a rare form of muscular stiffening that occurs at the moment of death, persists into the period of rigor mortis2 and can be mistaken for rigor mortis. The cause is unknown, but is usually associated with violent deaths happening under extremely physical circumstances with intense emotion.
Post-Mortum Movement or Twitching is another. The stored energy in our muscles doesn't just disappear at "death". And misfiring neurons or nerves can trigger muscles that have enough ATP stored up. You will see people that are dead twitch, move and spasm for hours after "death".
For some science, here's a dancing squid:
The Squid and Frogs muscles are twitching from autonomous reflex movement, triggered by sodium in the soy sauce, but this same movement can happen randomly from decaying cell misfires. Imagine the squid had a gun in its hand. All it takes is a finger to spasm.
Even certified diagnosed brain death doesn't stop it:
Many brain-dead patients have spontaneous movements such as jerking of fingers or bending of toes that can be disturbing to family members and health care professionals and even cause them to question the brain-death diagnosis. These movements occur in 39 percent of brain-dead patients, according to a study published in the January 11, 2000 issue of Neurology, the scientific journal of the American Academy of Neurology.
The doctors conducted additional tests and confirmed that there was no brain activity. “The living cells that were ordering these muscles to move were not brain cells or brain stem cells, but cells located in the spinal cord,” he said. “It‘s important for family members and health care professionals to be aware of this possibility.”
There's even a reflex named after it, Lazarus Sign:
Like the knee jerk reflex, the Lazarus sign is an example of a reflex mediated by a reflex arc – a neural pathway which passes via the spinal column but not through the brain. As a consequence the movement is possible in brain-dead patients whose organs have been kept functioning by life-support machines, precluding the use of complex involuntary motions as a test for brain activity. It has been suggested by neurologists studying the phenomenon that increased awareness of this and similar reflexes "may prevent delays in brain-dead diagnosis and misinterpretations."
In regards to sniping specifically, ideally they aim for the medulla oblongata to prevent Voluntary Muscle Movement. Essentially attempting to instantly turn the person into a paraplegic. Involuntary movement is still a problem.:
In a high-risk or instant-death hostage situation, police snipers may take head shots to ensure an instant kill. The snipers aim for the "apricot", or the medulla oblongata, located inside the head, a part of the brain that controls involuntary movement that lies at the base of the skull. Some ballistics and neurological researchers have argued that severing the spinal cord at an area near the second cervical vertebra is actually achieved, usually having the same effect of preventing voluntary motor activity, but the debate on the matter remains largely academic at present.
But the trope can be justified.
About half the time these the shows (always cop procedurals) introduce the hostage taker as having a Dead Man's Switch, a widely common trope. Unlike a trigger that needs to be pushed, a Dead Man's Switch needs to be released. Someone going limp from death is a problem when a Dead Man's Switch is used. Suicide Bombers have this often. It's a small scale version of Fail-Deadly. A gun could have a release trigger for example.