Two Arizona men are accused of driving to the event and opening fire, only to be shot by security.
The terror group has no direct evidence to prove their claim of responsibility and many experts don't believe it is very credible.
Meanwhile, the mother of one of the shooters is speaking out.
Nadir Soofi's mother said her son prayed five times a day, was clearly very serious about his Muslim faith, but she never suspected he would do anything like the attacks in Garland, Texas.
Soofi and 31-year-old Elton Simpson were shot by an off-duty police officer as they opened fire at an event outside Dallas where a Prophet Mohammed cartoon exhibition was being held.
"I don't blame the policeman that shot and killed him," said Nadir's mother.
Soofi is originally from Texas but moved to Phoenix years ago. Recently he operated a carpet cleaning business called Effinity Solutions. He lived in an unassuming north Phoenix apartment with the other accused shooter. The Federal Bureau of Investigation searched the apartment on Monday.
"They are looking for formal and informal affiliations with other people and organizations. They are looking for logistical planning for an attack. They are looking for components of weaponry and explosives, and frankly they are looking for information as to why the event actually occurred," said Richard Bloom with Embry-Riddle University.
Dr. Bloom is the director of terrorism, intelligence, and security at ERAU. He doubts ISIS's claim of responsibility for the actions of these two valley men.
"I think it is highly unlikely they are formally affiliated with ISIS or any other terrorist organization in any way," said Bloom.
FOX 10 has also learned that Elton Simpson graduated from Washington High School in Phoenix; he was part of the class of 2002.