I must admit to having a few self doubts, even though I have proof. What if there were 2 different families all sharing same names and date of birth. Nah-that's stretching it a bit, isn't it 
No, it is not stretching it a bit. Even in New South Wales, Australia, back when the population of the colony of NSW was about 70,000 (so about 1856) there were 'duplicated/triplicated' names of husband/wife and children. So, of that 69,173 people in NSW, ONLY 26,087 were born in Australasia (so born New Zealand, Tasmania, Victoria, South Australia, Western Australia or New South Wales including what became Queensland). There were how many

John and Mary Smith couples, with children named John, Mary, James, Jane, ..... well .... there were plenty... And same with John and Mary Brown and their 4 children, and Mr & Mrs Jones and their four children .....
http://www.rootschat.com/forum/index.php?topic=660501.0So even with such a small population base as NSW in 1850s in the middle of a gold rush, there were families with same names and sharing same dates of birth .....
To me, it is not at all un-expected that there will be possibilities of finding families with same dates of birth, same names etc....
Surely it is part of the challenge when enjoying family history research to strive to find ALL the possibilities and then using those same techniques to strive to eliminate as many as possible. All the while remembering that this is simply research, theory, and a non life threatening hobby.
Cheers, JM