It could get them out of a bind. Has a state funeral for the Thatch been formally announced - or the family could also decline it - there is precedent in this with Disraeli's and Nightingale's families turning down the opportunity. In other words, Richard III could provide them with the practice run they need ahead of the Queen popping her clogs - The Duke probably getting a Royal Ceremonial akin to the Queen Mum's or Di's. Not least he would be accorded with the 21 gun salute and not the 19 for a commoner.
How convenient - all it requires is for Thatch to live another 3 months as the DNA linkage is being made, one of hsi ancestors being on TV on the Beeb News as they swabbed him for a bit of goz for the test.