Yes, you can use copyrighted stills and archive footage for reporting an obit under fair use (as I understand it) but you can’t use it forever afterwards on the internet without clearing and coughing up, hence the blurring.
Under UK law you can legally use 'Fair Dealing' on moving content - for the purposes of reporting current events, criticism and review or quotation.
However you can't use that legislation on still images apart from for criticism and review (so you can fair deal a still if you are criticising its quality - say on a consumer programme covering a rogue wedding photographer who had taken badly framed pictures) but you can't just use any old still for news reporting purposes. If you could, press photographers would have no business. AIUI stills always need to be cleared and paid for if required (and not covered through blanket deals) - though news organisations may decide to 'await claim' (i.e. use it and pay for it later if someone pursues it)
Some stills agencies which broadcasters have subscriptions to may well purchase stills for obituary purposes and make them available to their subscribers - but they may have deals that don't allow them to be used online (outside of iPlayer/ITV Hub etc.)
News historically sail close to the wind and claim (I believe) mythical 'News access'/'Fair Use' etc. They don't always follow the letter of Fair Dealing law - but get away with it most of the time I believe.
Non-news shows are often a lot more careful. A strong sign of 'Fair Dealing' is when you see a credit for content that includes the writer/director and distributor/production company, as you have to credit the authors and owners of the original work.