People Magazine spoke to a source who said the pair didn't realize their actions were illegal.
"When they fight this, they're going to give a lot more nuance and mitigating circumstances that will help put their alleged actions into context," the source told the magazine. "The bottom line is that they just didn't realize that what they were doing was illegal."
The source said that the parents thought they were hiring a consultant to do what was needed and that it was similar to other parents "calling in favors, donating money to the alumni association, hiring consultants."
"When it all fell apart, nobody was as surprised as they were that they were in trouble," the source said.
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Loughlin and Giannulli pleaded not guilty earlier this month in the scandal known as Operation Varsity Blues. They were charged with conspiracy to commit money laundering, as well as conspiracy to commit mail fraud.
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Loughlin and Giannulli are accused of paying $500,000 in bribes to get their daughters admitted to the University of Southern California as crew recruits, even though neither is a rower.
If convicted, Loughlin and Giannulli could face up to 20 years in prison per charge.
The Associated Press and ABC News contributed to this report.