The supposition was part of a day of testimony in which the one-and-a-half pills the entertainer gave the former Temple University basketball staffer were intensely scrutinized.
The district attorney in Montgomery County, where Cosby is charged with three counts of aggravated indecent assault, revealed pieces of the 2005 civil deposition in which Cosby was asked why he concealed the pills' identity in a later phone conversation with Constand and her mother, Gianna.
"Why didn't you just say it was Benadryl?" a questioner had asked Cosby of the pills he supplied Constand before she claims he assaulted her in January 2004.
The performer had answered that it was self-protection, not deceit — he worried how Gianna Constand might use the information against him if he admitted it or sent the pills to her home in Ontario, as she had requested.
"I'm first thinking the mother is coming at me for being a dirty old man, which is bad," he said in the deposition regarding his conversation with the Constands. "But also: 'What did you give my daughter?' I put these things in the mail [to] Canada, what are they going to say if they receive it? What are they going to do if I tell them?"
Cosby said in the deposition that he gave Andrea Constand the Benadryl from his own reserve because she had complained about stress and neck pain and he wanted to help her relax.
Constand said the pills Cosby gave her were blue, yet when he voluntarily turned over Benadryl pills to police in January 2005 to demonstrate he kept a cache at hand, they were pink. James Reape, a Montgomery County police officer who investigated the case, said on the stand he "found that to be odd."
Prosecutors later in the day also read parts of the deposition in which Cosby acknowledged that decades ago he would buy Quaaludes he'd give to women before he would have sex with them.
"I used them the same as a person would, say, have a drink," he said in the deposition, adding that "there were times I wanted to have them just in case."
When asked whether he would "use them for young women you wanted to have sex with," he answered, "Yes," but said he never gave the drugs to a woman without her knowledge.
The Quaalude testimony is central to the prosecution's effort to shape the jury's impression of Cosby as someone who dispenses drugs to pave the way for sexual encounters. The defense had opposed the admission of the deposition in part because of that testimony, saying it wasn't relevant to the Constand incident.
Prosecutors on Friday also called a forensic toxicology expert, Timothy Rohrig, to testify that Constand's symptoms could be linked to a number of drugs, including both Quaaludes and Benadryl.
Rohrig said that even if the pills were Benadryl, one or one-and-a-half tablets would have a very sleep-inducing effect.
"Most people think of it as an antihistamine … but one of the actions is it can cause significant sedation," he said. He was asked whether the pills would be powerful enough for a specific criminal purpose.
"It has been used in a drug to facilitate sexual assault," Rohrig said, citing such cases.
Meanwhile, in the phone conversation with Gianna Constand, Cosby separately suggested setting up an educational trust for her daughter, who had expressed an interest in graduate school. Prosecutors implied that Cosby was trying to buy her silence.
"Have you ever used this vehicle of an educational trust … as a way of giving money to any other woman with whom you had a relationship?" he was asked in the deposition. He answered that he hadn't.
The jury on Friday also heard testimony from expert Veronique Valliere about why Constand didn't come forward for a year after the attack and maintained contact with Cosby, a key piece of the defense's strategy.
Called by the prosecution, Valliere, an expert on victim response to sexual assault, said that assumptions that a victim would end a relationship with an attacker are false.
"We have expectations that are misguided about how people react to sexual assault [by a non-stranger]" she said. Instead of cutting off all contact with a perpetrator, "the victim often wants to get that relationship right back to where it was nice and comfortable again."
She also said that reporting an assault to authorities is not necessarily a person's first response.
"Sometimes victims just want to forget about it, get through it and pretend it didn't happen for as long as they can."
Lead Cosby lawyer Brian McMonagle sought to discredit Valliere as biased, showing a Facebook post in which she cheered on an anti-Cosby pretrial ruling by writing, "Victory! The case goes on."
The prosecution rested after Rohrig, the toxicology witness, testified. The defense is likely to call several experts when the case resumes Monday. It remains an open question whether Cosby himself might testify. Most experts have long thought it extremely unlikely.
Outside the courthouse Friday afternoon, Cosby spokesman Andrew Wyatt left open the possibility. "We've not yet ruled out any of our options," he said.
3:10 p.m.: This article was updated with information on the lead defense lawyer attempting to discredit a sexual assault expert as biased.
1:25 p.m.: This article was updated with details about a deposition in which Cosby acknowledged buying Quaaludes he would give to women before having sex with them.