"There is so much personal information on them: A mother's maiden name, what they died from,"
Yeah, lets just ignore the obvious name, address, next of kin.. not sure if they put the burial location on there. Mothers maiden name is useful to a bank but not much use without the above.
Maybe they could have just added a filter to it? Kinda like looking up your flight details which isn't secure but pretty well filtered, all they need is ask for the deceased surname, date of death and postcode or similar and you'll be able to pull it up. It's not completely secure but then neither are flight details, just that the likelihood of guessing flight date, flight number AND surname are pretty slim