When I applied in 2013 I know I read on the official site (the previous iteration of it) that I couldn't look for work OR do work (paid or unpaid) while on my fiance visa, cause I sure would have been looking before I applied for FLR(M) if I thought I could. So it may be that it's old info floating around?
That's interesting, because I've just been looking on an archived version of the old website from 2010 and there's nothing on there that I can see that says you can't look for work on a fiance visa (the rules haven't changed in that respect since then - the section on employment being forbidden looks to have had the same wording then as it does now on the new UKVI website).
It says in the
employment section that if you are allowed to work then you can look for jobs via various different sources (newspapers, job centre etc.), but while it implies that only people who have permission to work should be looking for work (which is fair enough), I can't see anything on the site that says specifically that you can't look for work on a fiance visa in preparation for starting a job after you have FLR(M).
I've searched though the IDIs (Immigration Directorate Instructions) and the immigration rules from 2010 and there doesn't seem to be any mention of anything like that except that people with fiance visas cannot 'work' (i.e. undertake employment).
I'm not saying that it's something that you should do, I'm just saying that there's nothing in the rules that explicitly says you can't do it, at least not that I can find.
If someone without a visa can look for and apply for jobs from the US and then come over on a visitor visa to attend interviews with the hope of securing a Tier 2 work visa, I don't see why someone on a fiance visa who is living in the UK and will have permission to work anyway in a few weeks can't do something similar, even if it's just preparing your CV and searching online for vacancies.