Far from amateurish,
@Mandalas; I think these are really good questions.
So by way of background, to qualify in my SAR Nav role I've had to undertake a few qualifications which include touching on the maritime legal framework. Separate to this, my past background was in UK general law. So I have a little knowledge and happy to try and address some of the questions. In saying that, I'm not a specific maritime law expert by any means. So bear with my waffle!
Firstly, Chapter V of the SOLAS Covention Regs is the only section of the Regs that applies to all boats. The rest of it only applies to merchant ships. Chapter V doesn't lay out a Captain's specific responsibility in terms of crew (beyond awareness of their capability; roles and duties etc) as far as I understand; and doesn't specify obligations or actions in the sense of 'this is what you must do' should a member of their own crew go overboard.
To put SOLAS in context, it's been written at a high level and addresses the absolute minimum requirements of safety at sea. Given that it's an international convention, pitching it at a very basic high level allows countries to put more specifics into their own domestic laws if they wish.
There is a part of Chapter V that deals with obligation on distress situations, but the focus and wording of this seems to be round the duty of boats and their Captains to respond to distress calls, rather than dealing with specific response procedures to man overboard situations relating to their own vessel. Again, for context, the first ever SOLAS convention was put together following the Titanic disaster.
However, there are a few other international conventions that would be relevant if you consider the actions that RB would have been trained to take on believing a member of his crew has gone overboard, even if he didn't personally witness it. This is what I meant when I posted way back (I think it was in this thread) that there were certain actions I'd have expected him to take as he'd definitely have been trained in these. The main one is the STCW (The Standards of Training, Certification & Watchkeeping for Seafarers) which specifies the minimum training standards and expressly includes need for training in man overboard procedures. Again, this conveys minimum standard and countries are free to have equivalent certified training. In saying that, there is nowhere in a convention or law that I can see that specifically lists the actions you must take and I can see why, as boats may have different equipment available. But the actions I listed earlier in the thread are basically accepted standard actions covered by STCW certified training.
Plus, even though there is no specific written law stating what a Captain must do in event of a man overboard, that absolutely does not mean that a Captain does not have a duty of care. There has been a duty of care principle declared by the courts via case law which, to date, outlines an expectation that a Captain will take reasonable care to at least attempt a rescue, even though the rescue attempt itself doesn't have to be 'perfect' (Horsley v. MacLaren [1972], Canadian case, for any other nerds out there!).
Purely from an LE point of view in respect of the points above only, issue would be that they have no primary witnesses/evidence that Sarm went overboard. Then of course RB's version of events is that he searched for her himself.
Though I don't accept that they don't have enough circumstantial concerns to search the yacht in the first place.
Apologies again for this waffle; I've tried to outline the main requirements as best I can...