Case in point:
Even the Mayor of St. Louis (who has a verified account), where the Dorseys live, has joined the cause:
Verification on Twitter is designated by a blue and white check mark next to a user's name, and "is currently used to establish authenticity of identities on Twitter", according to the Twitter FAQs.
"Twitter proactively verifies accounts on an ongoing basis to make it easier for users to find who they’re looking for." It's an honor reserved for "highly sought users in music, acting, fashion, government, politics, religion, journalism, media, advertising, business, and other key interest areas."
Here is some of the information that the as-of-yet-unauthenticated Dorseys have been sharing lately:
It's not clear if the grandparents of Twitter qualify as the "general public" or not, but, according to Twitter, "We do not accept requests for verification from the general public."
"If you fall under one of the above categories and your Twitter account meets our qualifications for verification, we may reach out to you in the future."
Best of luck to the Dorseys on their quest for Internet authenticity.