I am very interested to see this thread, as I reported this problem to both Findmypast and The National Archives not long after their update of the 1939 Register in November 2016, when they opened 2 million more records.
As I understand it, when the Register was originally launched online, records for people born less than 100 years ago were closed unless they were marked deceased on the Register itself.
Some time after that, FindMyPast ran software which checked the closed records against the pre-1984 GRO death indexes, and the 1984-2007 GRO death indexes, which they have copies of on their site, using certain rules agreed with TNA to determine whether a match was unique or not, and if it was, the record could be opened. (They also open records regularly where birth dates become more than 100 years old.)
Then they used an outside agency to carry out a similar matching process against the post-2007 GRO death indexes, which FindMyPast do not have a copy of but which is supplied to certain companies. The 2 million records opened in November 2016 were the result of this last matching process, and as far as I know, FindMyPast staff have no way to check whether there is actually a death index record for people whose records were opened then, because they do not have access to the post-2007 death indexes - unless they visit one of the main libraries which hold them on microfiche.
I don't think there was a significant problem with the earlier updates based on matching against the pre-2007 indexes, only the post-2007 one. Both FindMyPast and TNA have denied that there was any problem with this update - see the most recent comments on TNA's 1939 Register blog for the discussion which I and a few other people had with them, until they closed it to further posts:
http://blog.nationalarchives.gov.uk/blog/1939-register-census-census/#commentsMost of the points I would make are in my comments on there, so I won't repeat it all on here as it would take ages and make this post much too long! But just to add that I have made a complaint to the Information Commissioners' Office and am waiting to hear the outcome.
Oh, can I also add that if you contact FindMyPast support to have a living person's record closed, they may not know how to do it properly and they may either redact it on the image or the index but leave one or other of those open, so it is best to go via clicking the button to have the record closed, but if you can't supply the ID proof which it still asks for, upload any image just so it will go through (e.g. a screenshot of the 1939 Register record or whatever) and explain in the text box how you know the person is alive. They have said that they don't require the ID proof any more, but for some reason they have not removed it from the webpage, so it doesn't go through unless you upload some kind of image.