This even though today, any of us could get on a computer and find persons with similar name, news stories of her vanishing, and the like.
PS Wonder how much money she had? Apparently she also owned a home
and (assuming there was only one Alice Perley) they could quickly have called her former broker (their brokers stay with them forever) and he would have known all about her circumstances (their brokers usually know the client quite well)...and that would have done it.
With no account number.