The 35 year old starred alongside the embattled comedian, who has been accused of sexual abuse and inappropriate behaviour in decades-old incidents by more than 20 women, on The Cosby Show from 1984 to 1992, and she has been left confused by the attacks on the funnyman.
Pulliam tells America's Today show she can only make judgements based on "the man that she knows".
She says, "I wasn't there, no one was there except for the two people to know exactly what happened (sic). All I can speak to is the man that I know and I love. The fact that he has been such an example and you can't take away from the great things he has done, the millions and millions of dollars he has given back to colleges and education and just what he did with The Cosby Show and how groundbreaking that was...
"Ultimately, they're just that, allegations, and it's very much been played out in the court of public opinion, but we're still in America, where ultimately you're innocent until proven guilty and I wasn't there. That's just not the man I know, so I can't speak to it."
On Sunday (04Jan15), Pulliam was eliminated from Donald Trump's reality competition show Celebrity Apprentice, in part, because she refused to reach out to Cosby for donations to her charity cause on the programme.
The Apprentice episode was filmed in March (14) - before any of the current and ongoing allegations against Cosby had emerged - and Pulliam explains she did not call her former Tv dad because she hasn't spoken to him in several years.
She explains, "Everyone assumes we're in this family that has dinner every Friday night, but the reality was, I hadn't spoken to Mr. Cosby and I felt that it would be tactless, you know, very rude to call somebody and be like, 'Hey, let me have some money right now'. And honestly, with the other cheques that I had lined up, I didn't feel that I needed to make that phone call."