Story highlights "We are investigating all aspects of the case," a police spokeswoman says

The victim, 33, has homophobic slurs carved into her skin

A neighbor says the woman came to her door in the middle of the night, naked and bleeding

An alleged victim of a hate crime in Nebraska spoke out publicly for the first time Thursday, the same day more than 1,000 people rallied in her support in Omaha.

"I can't adequately express how much it has meant to me that people are standing with me and people are standing for me," Charlie Rogers, 33, told CNN affiliate KETV.

Three masked men allegedly bound Rogers and carved homophobic slurs into her skin Sunday, Lincoln police said. The incident has been classified as a hate crime because derogatory terms for lesbians were used, said Officer Katie Flood, a spokeswoman for the Lincoln Police Department.

Rogers said she kept her identity secret in the immediate aftermath of the incident, but decided to go public to refute any suggestion that the attack did not happen.

"For people to think this doesn't happen here, it does," Rogers said. "It did."

Her attorney, Megan Mikolajczyk, told CNN that Rogers wanted to make it clear it was not a hoax. Asked if they were addressing anyone specific, Mikolajczyk said they were not, but she added she wasn't surprised there were naysayers.

"I don't think it's safe or necessary to point the finger at any one individual," Mikolajczyk said. "I think it's par for the course for any sort of high-profile incident for people to question what happened."

In response to a question from a reporter, police spokeswoman Flood said, "We are investigating all aspects of the case, including the possibility that it is a false report. This type of evaluation is not uncommon and is necessary in completing an investigation."

Rogers said that she escaped after the attack and ran to the nearby home of Linda Rappl. "I was in shock," Rappl said. "She was naked, her hands were tied with zip ties. All I could see was a cut across her forehead and blood running down."