Why did Aaron Stampler receive that verdict?

Because when you take a look at both characters, it's hard to believe it is an act, and you believe that he is actually insane.

So, after Aaron turned into Roy and attacked Janet Venbale, and then after being knocked to the ground by the guards, he turns back into Aaron, proving everyone he has Multiple Personality Disorder and is actually insane. The judge sends Aaron to the hospital under reason of insanity for 30 days to get the help he needs. Then as we figure out later, he's faking it the entire time.

If you're asking why couldn't he be arrested for it, after admitting that he actually killed the archbishop and faked the disorder, it is called double jeopardy. The Fifth Amendment to the United States Constitution provides:

[N]or shall any person be subject for the same offence to be twice put in jeopardy of life or limb. ... "

Conversely, double jeopardy comes with a key exception, which means he can't be trialed again for it.

In 1993, when the book was published, neither courts nor dissociative identity disorder (DID) worked as they do today. DID was considered in 2008 to be

one of the most controversial psychiatric disorders, with no clear consensus on diagnostic criteria or treatment.

I'm no law expert, so I can't address the realism (or lack-there-of) of this scene, where a single expert classifies Aaron as having DID, and the court believes it. However, going by the movie's plot, the jury has, as evidence,

• Molly Arrington, the psychiatrist examining Aaron, is convinced that he suffers from multiple personality disorder caused by years of abuse at the hands of his father
• Vail slowly sets up a confrontation in court by dropping hints about the Archbishop's pedophilia, as well as Stampler's multiple personalities.
• After Venable questions him harshly during cross-examination, Stampler turns into "Roy" in open court and attacks her, threatening to snap her neck if anyone comes near him. He is subdued by courthouse marshals and rushed back to his holding cell.

The entire trial was set up by Vail to slowly turn the jury's opinion towards insanity.

Aaron is shown as a sweet scared church boy, who (unbelievably) turns into Roy, the violent sociopath. In a time where DID wasn't as well as know as it is today (which is still not that well-known), the expert's opinion and the (great) performance of Aaron makes it believable, and leads to the decision of

not guilty by reason of insanity, remanding him to a maximum security mental hospital.