You have to remember that the British Museum did not have a duty to report anything to the public.They were commissioned by the owners of the Shroud to date it, which they did, and no doubt returned their full results to those who commissioned it. The paper published in Nature was a comprehensive account of the process, with the same calculations being carried out for the Tucson results as the other two universities, as I explained.
When assessing the range of results from an experiment statistically, the range is theoretically infinite, regardless of the highest and lowest result. The best one can do is to assess the probability of any particular result being the true one. This concentrates around the middle, while the outer ones are increasingly unlikely. The range quoted in Nature report, was two standard deviations away from 1325 AD, which is a standard way of giving the most likely probability. All the measurements, including the Tucson one of 540 BP, fall within three standard deviations of from the mean.
As for your query, I did address it. A date of 795 BP (Before Present) does not represent a calendar date. It is a straight mathematical conversion of a ratio of C14 to a number of years of decay, from 1950. (Not 1988 - for convenience and uniformity, all BP dates are ‘as from’ 1950). In order to convert it to a calendar date it must be referred to a calibration graph, such as the one used by OxCal, the online version. 795 BP is equivalent to about 1240 AD.
The British Museum did not misrepresent the results of the dating, and the STuRP investigation did not prove that the Shroud was miraculous,