Hi Jon I got my SETV there back in April, and used a lease agreement with no problems. Taking the additional docs as per Tod's suggestion above can't harm though.
Also worth remembering to take copies of any docs that you submit as the only thing you get back is your passport.
Finnair aren't amazing. I arrived in Bangkok 3 days before my luggage last year and got a 100 Euro voucher and 500 grams of cured salmon by way of compensation.
Could be - speaking from personal experience I've needed 5 business visas in the last 12 years and always flew out to get them - also never needed a background check for a visa or a work permit. But as you say - things are inconsistent here.