Could the people getting hot under the collar and shouting 'scandal' please reflect on the possible implications of their actions on future access to new recordsets.
I can understand the anguish and frustration caused by finding the implied death of a close relative and being asked to prove they are still alive. I can also understand the concern about protecting potentially vulnerable people from identity fraud and scams.
However, if you take a handwritten dataset which potentially has living people included and seek to place that information online in a searchable form then it is virtually impossible to ensure that absolutely no living people's details will be included in the published data. Seeking to achieve 100% accuracy in the process would mean it is not economically viable.
If the people complaining loudly are listened to the next time there is a dataset including potentially alive people then those people in charge who are quite happy to keep all data hidden will be able to point to the "terrible invasion of privacy" which the 1939 Register was as justification to keep 'their' data hidden because just one mistake could lead to compensation claims etc.
In real terms the published data on the 1939 Register does not pose much of a security risk. Married names and maiden names are easily found by other methods. As Clairec666 points out, DoB (the 'correct' one!) can be obtained by ordering a certificate - and indeed is readily available online for anyone who has been a UK company director. Having an incorrect DoB opened on the 1939 Register could even be a security benefit as any fraudster who decided to use those details may well trip anti-fraud alarms!
In the last couple of years I've opened many new bank accounts - the information you need to provide is substantially more than name, address and date of birth. The information you provide is verified against databases and cross-checked - even for opening savings accounts. I had one application rejected because the word I gave for 'mother's maiden name' did not match the record held in a third-party database.

(Not surprising as my Mmn changes with every bank!)
It is very difficult to get a credit card or loan if you don't have a quite active credit history - this in itself is likely to be a protection for our older vulnerable relatives.
Fraudsters are business people, time is money. They are unlikely to spend hours trawling through the 1939 Register to identify someone whose record has been opened in error in order to find out their (possibly incorrect) date of birth. There are far more economically efficient ways of getting ID's to scam!
So please, don't shout too loudly that records are open which should be closed. So long as FindMyPast take a reasonable approach to closing incorrectly opened records that should be enough. And yes, 'reasonable' should include checking to ensure the person asking for the (re)closure has the authority to ask. Imagine the outrage you'd feel if you discovered FindMyPast had closed your ancestor's record because a stranger had made a mistake, or made a malicious request?