I'm not that keen on the phrase "double opt-in". It's a phrase used by marketers, to make it look as if anti-spammers are doubling their workload and making things unnecessarily complicated.

What you are referring to should be called "confirmed opt-in", and it simply means that you don't accept an opt-in unless you can be sure it came from the owner of the mailbox in question, and was not forged. Making people opt-in twice wouldn't help with that.