But it is that simple. In my case, I got a card for a family member. But there is no verification done so you can literally get a card with any name on it. It is still tied to your identity through the bank.
I also checked US Bank and American Express and you are correct, the process is not smooth at all. US Bank wants me to print, sign, and mail it! American Express wants to verify identity of the additional user using an SSN. That makes no sense of course, because they might not even have an SSN and the main account holder is still contractually obliged to pay the account balance.
Since you don't have an annual fee, can you order a card in the name of Donttrackme McSpammer (or any other similar name that couldn't be mistaken for a real name) and see if you get it?
Thanks for having taken the time to check the other two sites as well. I appreciate it!