Trew released a statement on Friday ... saying, "Chris and I are deeply saddened that we have brought negative attention upon our family, friends, and the University of Texas, among others. As Chris’ fiancée and biggest supporter, I apologize for the role I played in this unfortunate event."

She continued ... "I realize that my frustration when breaking his glasses initiated a physical struggle between Chris and myself. Chris did not strangle me, and I told that to law enforcement that evening."

As we previously reported, Chris, 49, was arrested in Texas after law enforcement officials charged him with a felony -- assault on a member of a family or household by impeding breath circulation.

According to court documents, Trew alleged that she and Beard had been upset at each other for a few days and were having "relationship issues" -- and claimed things finally reached a boiling point with Chris slapping reading glasses off her face and choking her with his arm.

Police said in the docs they observed visible teeth marks and redness on Randi's right forearm and an abrasion on her right eyebrow and leg. They also noted a cut to her left thumb.

"Chris has stated that he was acting in self-defense, and I do not refute that,” Trew’s statement continued. “I do not believe Chris was trying to intentionally harm me in any way. It was never my intent to have him arrested or prosecuted. We appreciate everyone’s support and prayers during this difficult time."

Beard posted a $10,000 bond and was released from custody.