In telling of the tense encounter, she asserted Natalee was sexually assaulted before she vanished.
Twitty says she was tipped by a member of the media that Deepak Kalpoe was working at a local Internet café, and wasted no time confronting him Monday.
Kalpoe, 21, and brother Satish Kalpoe, 18, were among the last three people spotted in public with Natalee before the Alabama teen disappeared in the early hours of May 30 on the final night of a high school graduation trip to the island.
The third person, Dutch teen Joran van der Sloot, is the only suspect still being held in connection with Natalee's disappearance. Both Kalpoe brothers were kept in custody for a short time early in the investigation.
Twitty has said the Kalpoes know more than they're telling investigators.
Twitty described her close-up with Deepak to CBS News:
"There were customers on the computer and he was seated behind the cash register, and I guess he thought he was going to have a normal day at work.
"I wanted to ask him, Joran had admitted sexual assaults that he had committed against Natalee, and I wanted to ask Deepak: Did he participate, or did he try to help her?
"He couldn't answer me. He could only look down at the ground."
"I saw his eyelids pretty much the whole time that I was there, and I would have to tell him to hold your head up and look at me when I'm speaking with you.
"He couldn't do that. He would either not respond or he would just tell me that his lawyer had advised him not to speak with me.
"I expected him, if he had no involvement, if he was not a participant in the sexual acts committed against my daughter, that yes, he could have come forward and said, 'No,' and looked me in the eye. He couldn't do that.
"I let him know, under no circumstances, that there is nothing that I'm going to refrain from asking, and I'm going to ask every question, and I'm going to stop at nothing, and I will continue to.
"And he said, 'The media hasn't seen this side of you.' And I said, I've been saving it for you, Deepak.
"I'm always going to hold out hope, no matter how bad it looks. You can't prepare yourself for that, and I don't have to."
Twitty also says she believes there was a level of ineptitude on the part of Aruban authorities, but she's more optimistic, now that a group of investigators from Holland has become involved.