Absolutely, I agree but with no real defence (in my opinion) I suspect they will clutch at any straws they can and when you consider the content of the family witness statements during opening statements, this sadly suggests to me the defence are planning to use her mental health. I very much hope I am wrong but if defence are arguing their client didn't put her in the river then i suspect they will put forward an alternative suggestion. As pointed out by someone else earlier in this thread she was discharged from the mental health team and have friends and family saying she was in a good place so I suspect it will be easily rebuffed but I still think it will be raised. Fingers crossed I'm wrong.They don't have to prove anything of course.
But contentions from counsel require an evidential foundation - otherwise they are mere speculation. So in practice, an evidential onus arises on the defence if they wish to convince the jury of a version - otherwise it is mere unsupported conjecture from counsel.