KANSAS CITY, Mo. » The mother of a missing Missouri baby may not be casting herself in the best light by telling national media that she drank heavily the night her daughter disappeared and other unflattering details, but her honesty shows that she and her family "have nothing to hide," her attorney said.

Deborah Bradley told television audiences Monday that she may have blacked out in the hours before she and Jeremy Irwin reported that their 10-month-old daughter, Lisa Irwin, was missing from their Kansas City home early Oct. 4. Bradley also now says she last saw her daughter hours earlier than she originally told police.

"I don’t recall in recent history anyone under this umbrella of suspicion be so open and forthright, warts and all, regarding the events. Because they have nothing to hide," said attorney Joe Tacopina, who held a press conference Monday to announce he had been hired to represent the couple.

The parents reported their daughter missing after Irwin returned home from working a night shift and found the front door unlocked, the house lights on, a window tampered with and the baby gone. Bradley and their two sons were asleep elsewhere in the house.

Police have said they have no suspects in the case and no major leads. On Monday, the parents allowed the FBI to bring tracking dogs through their home. The FBI also searched a neighbor’s house with the dogs, as well as the yard of the home where Bradley and Irwin have been staying with their two sons.

Bradley had said in previous days that she checked on Lisa at 10:30 p.m. on Oct. 3, but on Monday told NBC’s "Today" show that she actually last saw Lisa when she put her to bed at 6:40 p.m. She did not explain why she changed her story.

Bradley told Fox News that she got drunk after she put her daughter to bed that night and may have blacked out. She said she "probably" drank more than five glasses of wine, and said she frequently drank at home after her children were safely in bed. She also said she had taken a dose of anti-anxiety medication that day.

Bradley told NBC that police accused her of killing Lisa, but she insisted again that she had not harmed her daughter.

"No, no. … I don’t think alcohol changes a person enough to do something like that," she said.

Tacopina, who also defended Joran Van der Sloot, the Dutch man suspected in the 2005 disappearance of Natalee Holloway in Aruba, said Bradley detailing her drinking the night Lisa went missing "goes to her credibility."

"That’s something she was willing to tell the truth about even if it didn’t make her look good because she’s got nothing to hide," said Tacopina, who refused to say who was paying him and would only say that he had been hired to counsel the parents through the investigation.

Sean O’Brien, associate professor of law at University of Missouri-Kansas City, said it was difficult to read anything into Bradley’s remarks about her drinking or about what police told her. But he said it was wise for the parents to hire a lawyer, and they likely should have done so earlier given what Bradley has said about police accusing her of being involved in the baby’s disappearance.

"When the questioning becomes accusatory … it’s time to shut up and lawyer up," O’Brien said.

But he noted that police remain the family’s "best hope" of finding the baby, so Bradley would want to continue cooperating.