If a local business had a website verified in the Google Search Console prior to verifying in Local, Google would on occasion auto verify the local listing without the need for a post card or phone call.
Previously this would just happen with no forward facing interface and would often be a surprise to the claimant.
Now, according to this screen shot captured by Avinash Murthy (@avinash4dvg) it appears that there is now a viable interface choice to allow for instant verification when it is available.
This option has not been readily available to most businesses and even those with a common log-in and a verified Search Console site were not always offered the option. Here’s hoping that this new interface upgrade means that Google will be extending the program more broadly.Google MyBusiness Now Surfacing Web Verify Option by Mike Blumenthal