If there was one thing I would change it would be the blackmail, the blackmail doesn't make sense considering he was committing a crime and she was obviously unconscious if instead she did drunk sex acts on him maybe mistaking him for he bf and he was secretly recording or taking pics then that would be good blackmail. currently she could just call the police and have him arrested and use the pic as proof.
Blackmail as NTR setup is always difficult. It usually requires the FMC to be extremely gullible or naive.
In this case though, I think it works quite well though. Liz doesn't have any evidence, it's unlikely Matt would have actually send the picture to her. He only needs to let her see it on his phone. DNA evidence would have been destroyed the next day when she showered and washed her clothes.
If she did go to the police, they might very much dismiss her story as a guilty cheating girlfriend trying to "fix" her mistake.
New managers in companies also regularly fire old employees, so even if Liz trusted MC to believe in her, she might still fear for her job. We've heard that she's barely scraping by. How much would she really trust a boyfriend she hasn't even had sex with at the time?
All in all, I believe Liz' situation leaves enough room for fear and doubt, that succumbing to blackmail might actually have been an understandable decision.
Matt might even have thrown her a bone and allowed her to refuse any actual intercourse. He's definetely confident enough to believe he'll be able to make Liz ask for sex herself.
With that admission, I do believe Liz might just have thought that she'd be able to deal with Matt until she finds a better solution. Gathers evidence, looks for another job etc.