Double optin is advised but not required. It's outlined as a guideline for use with shortcode primarily. 

You can read the entire guidelines here

The core key compliance requirement is ensuring that the recipients of your text messages (your recipients) have expressly consented or “opted-in” to receiving text messages as part of your campaign.

There are examples more specifically of opting in via phone versus web app: 

This is why we send out the initial compliance text conveying what it's for and they may receive (insert frequency amount) of sms messages per month.