What registration process can one employ to prevent users from creating more than one account?

I am working closely with a local entity and they want a registration process for their site visitors. However, they do not want people to create fake accounts using throw-away email addresses, etc.

They are considering using something like Facebook to authenticate a user because Facebook does all of the vetting ahead of time to ensure that a person is pretty darn close to the real thing, which assures this company that their new users aren't made up. Basically, if you don't have a Facebook account, you can't log into our site and participate in the community - it's all or nothing.

The problem I'm facing is that the owner of the company doesn't want to require his users to have a Facebook account. Most of his friends don't have one and neither does he.

Is there another sign-in option out there that is pretty darn close to making sure that legitimate people are given access to the site? I know Twitter, AppleID, and Google also have sign-in options but they're not really any better at vetting a user.

I know I have difficulty cheating a registration process if I'm required to give my mobile number but I've never set something like that up so I'm not sure what additional services (text a code to login) would be required and how much that would cost.

Is Facebook the only decent option out there to accomplish his goal of preventing fake accounts?