Oddly enough the organisation I work for is trying exactly this tactic. They are constantly demanding line managers to require staff to talk to them about very personal issues relating to their mental health and stress triggers - which is frankly prying and none of their damned business unless it's affecting their ability to do their work - so that they can tick the box saying they've taking everyone's mental health seriously.
It's a preposterous crock of shit, given that they're a bunch of utterly ruthless bastards who have fostered a nasty environment of bullying and micro-management. They're also quite capable of taking confidences about our mental health and using them against us.
So, for me, this struck a chord. Of course I'm not suggesting for a moment that this mother-in-law is equally ruthless, but I do fully understand how threatening it feels when some unqualified bystander seems to take a doctors' mantle upon themselves to armchair-diagnose someone else's mental health. It must be especially discombobulating when they then decide on a narrative (of course with themselves at front and centre) as to how the situation they've dreamed up should best be dealt with.
It's not what MiL has done, but the way she's gone about doing it. You don't issue diktats to others about the state of their mental health. That sort of behaviour crosses the line, as it can actually be harmful.
It may be she's genuinely concerned, is just a rubbish communicator, and has made an (in my view serious) error of judgement. In which case she'll be quite understanding if you tell her 'No thank you MiL, I have no issue with my mental health and am not given to confidences. But if you'd like to help support us, I'd be delighted if you could do X, Y, or Z'.
That gives her a job and makes her feel useful. You'll also be able go gauge a lot by her reactions. If they are benign, and she happily accepts what you say about the kind of support you'd like rather than she deems appropriate, then everything is A-okay. If she kicks off or starts down the passive aggressive tack then you'll know how right you were to have been wary of her in the first place.