The following contains spoilers for She-Hulk: Attorney at Law Season 1, Episode 1, "A Normal Amount of Rage," streaming on Disney+.
Comic book stories are science fiction, specifically when the origin of the hero involves a scientific concept. Today, everything is "nano-" or "quantum-" with sci-fi science, but back in the day it was good old radiation that did the trick. In She-Hulk: Attorney at Law's series premiere, the storytellers use both old and new sci-fi justifications for why not just anyone can become a Hulk.
Science fiction storytellers have to decide just how scientifically accurate they want to be. Some shows like The Expanse are strict in their adherence to the laws of physics. Other franchises like Star Wars simply replace "magic" with "science." Marvel Comics always played its stories down the middle of these two divides. Spider-Man, The Fantastic Four and the Hulk all owe their superpowers to radiation, but how it affects them is not even close to scientifically accurate. Since the world now knows that exposure to intense amounts of radiation are nothing but lethal, She-Hulk: Attorney at Law gives us a new sci-fi syllogism to explain it.
Back in The Avengers, Mark Ruffalo's first Hulkish outing, Robert Downey, Jr.'s Tony Stark told Bruce "that much gamma exposure should have killed you." Banner responds dismissively to the idea that the Hulk saved his life. It's a lovely sentiment, but not great science. When The Savage She-Hulk debuted in the 1970s, she got her powers from a blood transfusion after a car accident. She-Hulk: Attorney at Law honors this origin -- though instead of a deliberate move to save her life, this transfer of gamma-blood is accidental. In the preceding scene, Bruce explains healing his Endgame arm injury with a device that keeps him in human form. In the crash, the device is damaged before his blood mixes with his cousin's as she tries to save his life.
In the 1970s, knowledge of hematology wasn't as expansive. Again, given what's known about radiation, gamma-irradiated blood wouldn't give someone powers... just a painful death. The real cutting-edge biology of today, however, is genetic study. Thus, when Smart Hulk tells Jen she took in a lethal dose of gamma radiation, she freaks out like anyone else would. The moment is played for laughs, as Bruce goes on to explain why she (and himself) are big, green and powerful instead of super-dead. "You and I," he explains, "share a rare combination of genetic factors that allow us to synthesize gamma radiation into somethin' else." In this case, "somethin' else" means "sci-fi magic."
Smart Hulk then goes on to describe that Jen's blood is able to synthesize gamma radiation differently than his does. It's one of the main ways She-Hulk: Attorney at Law highlights how Jen is a superior Hulk to Bruce. The how of this fact isn't really all that important to the story, but the 'science' is there to help explain why. It's a twist of luck that both Bruce and Jen didn't die from gamma exposure, and an equally lucky break that Jen's "rare genetic factors" work so much better than Bruce's.
This explains why every mad person in the MCU isn't out there blasting themselves with gamma radiation to become unstoppable rage monsters. Still, because anything can happen in a comic book world, Bruce destroys Jen's blood samples just in case there is "a one million percent chance" someone could use it to give themselves these sorts of powers. For the nitpicky viewer, this may not be a satisfying answer, but it's a more rigorous one than usually given in these stories. Remember, Jamie Foxx's Max Dillon became Electro after falling into a vat of electric eels. Using just enough scientific vaguery, She-Hulk: Attorney at Law provides justification for the title character's powers for all viewers except those who refuse to accept any kind of fictional kookiness in their superhero stories.
The decision to keep the ability to turn into a Hulk rare is a good idea in the MCU. There can be others who are able to synthesize the gamma in similar ways, such as Tim Roth's Emil Blonsky or Amadeus Cho, whenever he's cast, but it keeps the power feeling special. It's a satisfying enough answer to the question of who can become a Hulk without getting mired in too deep with sci-fi technobabble.
See if anyone else Hulks out in She-Hulk: Attorney at Law which debuts new episodes Thursdays on Disney+.