White successfully dodged a charge of first-degree murder. In the aftermath, people struggled to understand why White had received such a lenient sentence for such an awful crime -- and they found it in the "twinkie defense," in which White's lawyers argued that he committed the murders because he overindulged on sugary snacks.
Except, it's bullshit. At trial, White's lawyers did indeed argue that White was suffering from diminished capacity. And not because he'd gone on a sponge cake binge, but because he was suffering from severe depression as a result of his dismissal, which left him incapable of moral judgments and ergo, premeditation. This depression manifested itself, according to a psychiatrist testifying for the defense, by White casting aside his healthy, clean-cut lifestyle to dress slovenly, grow a beard, and indulge in junk food ... a series of choices which made White even more depressed, and (according to the defense) resulted in him killing two people as payback.
While the defense did mention junk food, this was all only done in the context of proving White was suffering from depression. He didn't eat a snack and then go on a murder spree (and we don't think any snack is capable of doing, save for the Popeye's Chicken Sandwich).
In nutshell, White got off with a lesser charge of manslaughter because the defense successfully demonstrated to the satisfaction of the the jury that White -- who they even acknowledged as being guilty in their closing argument -- was suffering from diminished capacity and had only acted in "the heat of passion [...] which fogs judgment." The idea of the "twinkie defense" later emerged as a counter-narrative (and hack comedians' go-to anecdote about how the legal system is a sham).