"Bulletproof". They forgot to specify outline: none; border: none; on the img and a tags, among other things. You're going to have a big ugly border around all your social icons in some email clients. They also fail to specify which email clients fall under "all the email clients that matter". I'm assuming hotmail/outlook, gmail, yahoo? But what about native android and native iphone clients? Android 2.2 or 4.0+? iPad? Surface? Email development is hell, and I'm all for services that help with that, but not ones that brush off the details with big promises.
I used Litmus to test email compatibility of the buttons. Just checked again and you are correct. A border shows up in one of the older Android Gmail clients, but it works in all the rest. Even Lotus Notes 8, Blackberry, and Outlook 2000 :)
I'll update the example to fix. Thanks for pointing that out.