His jaw dropped half-way through when he asked for my wife's and my phone number, and I had to tell him that I don't own a smart phone.
Turns out you must have a smart phone because the system sends you some kind of code to verify your identity. Let that sink in: I am sitting in front of the clerk, but in order to identify me, he needs me to give him some phone number.
The only way we could finalize the application is by me asking my mother whether I could use her phone number briefly to get this over with. She forwared the code to my wife's phone. That worked in the end -- but so much for "identifying me".