Cyborg isn't in UFC strictly because of Tito. UFC and Cyborg had an agreement where she'd be under contract with them but could fight in Invicta until she could make it down to 135 lbs. Then Tito started his crap holding press conferences saying she'd die if she made it to 135 lbs.
UFC had a contract with her due to the Strike Force buy out. Dana wasn't really interested in women's MMA initially. It wasn't until Rhousey began generate buzz that he changed his mind and brought her over to the UFC and created the women's 135.
Dana has gone on record saying he'd be willing to give her a contract if she can make 135 since it would mean a match against Rhousey, which would probably be the biggest drawing women's MMA fight.
You're right. There was the initial Issue with Tito and the weight cut.
Tito isn't her manager anymore.
There's no money in a catch weight fight since there isn't a 145 division. If Cyborg wins the catch weight fight, there's nothing to do with Cyborg thereafter.
If she beats Rhonda, she makes Rhousey look weak, whereas if Cyborg wins a 135 title shot then they can book her in fights with Cupcake, Cat, etc.
It's that simple. Dana is willing to sign her with Shannon Knapps blessing.