The photo, which showed the singer's body in an open casket, surfaced after the funeral service and ran in the National Enquirer.
Carolyn Whigham, the owner of Whigham Funeral Home, and two pastors said they do know the person who took the photo, but they aren't identifying the person. They said that's up to the Houston family.
Whigham told The Star-Ledger of Newark on Thursday that her home "had no role in this shameful betrayal." She was responding to what she says are claims that either she or her employees were involved.
Houston, 48, died Feb. 11 in a Beverly Hills hotel room. The cause of her death remains under investigation.
Whigham says she determined the photo was taken Feb. 17, a day before the funeral.
The Associated Press contributed to this report.