Cox said he understood that Kyle and Littlefield were helping Routh work through his own PTSD, but that he did not know how they came into contact. He said it was not a FITCO session.
Erath County Sheriff Tommy Bryant on Sunday offered a similar description of the situation.
"It's my understanding that the suspect may have been suffering from some type of mental illness from being in the military himself," he said of Routh.
He said Routh's mother may have reached out to Kyle for help with her son.
"We kind of have an idea that maybe that's why they were at the range for some type of therapy that Mr. Kyle assists people with," Bryant said.
Bryant didn't know whether Routh was on any medication or whether he had been diagnosed with post-traumatic stress disorder.
Authorities say the three men arrived at the Rough Creek Lodge southwest of Fort Worth around 3:15 p.m. Saturday. A hunting guide discovered the bodies of Kyle and Littlefield around 5 p.m. and called 911.
Routh allegedly left in Kyle's pickup and went to his sister's in Midlothian. He told what he had done and left. She called police and Routh was eventually found at his home in Lancaster. After a short pursuit he was arrested.
Routh was being held on $3 million bail in the Erath County Jail. Authorities said they believed he had requested a court-appointed attorney. Calls to his home were not answered Sunday.
Kyle was also president of a security training firm Craft International. Craft had scheduled a $2,950-per-person civilian training event at Rough Creek Lodge called the "Rough Creek Shoot Out!" for March 1-3. The price included lodging, meals and shooting instruction. Kyle was scheduled to teach the first class, called "precision rifle."