As I've said a few times, I was contact with them. Mainly out of curiosity. They seemed serious enough. Asked all the right questions and concluded they didn't have anything for me.
Back when I researched this, I never saw any mention of a letter from immigration. It's not really the problem they're addressing. The embassy letter shows you are who your passport says. Certified by your country(!) Issues they're worried about is like international fraud and such.
Again, you need one from the embassy (sort of confirming you are who your passport says.)
My experience from Bangkok Bank, EmQuartier: I hand the guy my passport and as I'm sitting down and messing around my dunnage, he suspiciously goes "hmm, Denmark..." I pull out the embassy letter and say "also have this from my embassy" and he lights up like a xmas tree and goes right ahead. I was on a tourist visa at the time. But I don't think he even checked that.