I think I know what means though. Amber has a sort of ‘Oh, I need to write this down, so I’ll remember’ vibe, when everyone knows that musical theatre is her job and she must learn routines all the time. It just doesn’t feel genuine and try too hard.
I'm not sure why this makes her fake. Some of the pros do write things down to plan their choreography. Case in point, Lewis has an Insta story right now showing a paper bag with Katya's notes on their dance.
I don't find Amber fake. Being one of the best dancers remaining doesn't mean you'll be top of the leaderboard and avoid the dance off. She is under pressure to please both judges and audience, and having been in the dance off before, she knows it can happen again.
I have also seen Lewis called cocky in here, but again, I don't see it. As competitive individuals, he and Katya obviously work incredibly hard at perfecting every detail of their routines, so he must be elated to see their efforts rewarded.
I've been on YouTube to have a look at his Ruff Diamonds video, and he is utterly mesmerising to watch even as a teenager.