Would the RusFed really allow it? And do you really think another coach would work for her?
She has to be able to pay for it herself, which is not a small amount at all. If she can, I think she can go.
As for another coach, well look. I have as a whole, no major issues with Eteri. But in a year's time, where will they be? Trusova, Kostornaya, Anna S, Tarakanova, all seniors. Do you really think the Fed won't be pushing for those kids? And Eteri is a Fed coach. Look at how they dropped Zhenya this season, like a hot potato. Once not one, but all of them switch over, do you really think the Fed will care about one Zhenya Medvedeva? They care about medals and 'certain bets'. She will be fighting for spots, never mind anything else. Eteri herself doesn't have the best of views on the longevity of female skaters and how long will she hold on to Zhenya with new blood coming in?
So one of the ways to get around that, or at least try, is to get to a coach who can help her primarily technically and who isn't Fed dependent. She doesn't need Daniil. She can finally go abroad and get choreo from any top choreographer. But technically, someone strong enough in the field to work on her jumps is at this point what she can focus on. (It's kind of a pity Raf is out of the question now because he's good for the jumps, not so good for the rest but that's all right for her current self).
This really is about Zhenya and what her long-term outlook is and I don't see anything good there if she stays with Eteri. She has simply aged out of it, considering their system. But if she wants to jump ship, the time is now, so that she can have at least one season to adjust with only Alina there, before the others come in.
If she stays, she stays, and everything crossed.
As for the rumors and it's never ever happening.
Yeah, and she wasn't injured, and everything was all right and those silly rumors are not true stop it. How did that work out?
It would be highly surprising if these particular rumors are true as it would be very difficult to resolve the two issues I mentioned up there, even if she wants to, but what people say in public is never a reason to go - oh they're not true. They're public figures and nothing should be taken at face value. Difficulties involved with her potential leaving are a far bigger reason to think they're not true.