Botham Jean's family says he did not know or have a relationship with Officer Amber Guyger

The family of a black man who was fatally shot inside his own apartment by an off-duty, white cop in Dallas wants to put one rumor to rest. Botham Jean's family says he did not know or have a relationship with the officer who shot him.

CBS News' Omar Villafranca spoke with Jean's family, who says they don't think Dallas police officer Amber Guyger is telling the whole story about what happened in that apartment building last Thursday. The family is still "lost" as to what happened that night. 

Guyger told investigators that she went to what she thought was her third floor apartment. Instead, the 30-year-old went to Jean's fourth floor apartment directly above hers. Guyger says the door was "ajar" and inside noticed "the apartment interior was nearly completely dark."

"To hear that his door was open, he would never -- and have the lights off -- he would never do that," said Allisa, Botham's sister. "He was like me. He does not like the dark."

Believing Botham to be a burglar, Guyger says she gave "verbal commands that were ignored" then "fired her handgun two times," hitting him once in the torso. It wasn't until Guyger "turned on the…lights" and "called 911" that she realized she was "at the wrong apartment."

The family says Botham placed a red carpet in front of his door to distinguish his apartment from others.

"He made sure to let everyone know this is mine – it's my red carpet," Allisa said.

Botham grew up in St. Lucia but his brother, Brandt, says that he was well aware of racial tensions in America.

"He said to me as a black man in Dallas, you don't walk with your hands in your pockets. Just so you don't get any profiling," Brandt said.

Guyger has been charged with manslaughter, but some demonstrators want her charged with murder. A grand jury will ultimately decide whether Guyger's charges get bumped up. Her attorney denied CBS News' request for comment. 

A funeral for Botham is being held on Thursday.