They do!
You rock up to the German, Dutch or Spanish Embassy with your 1 day old passport and 5 day LT Farang sponsor in tow
Fill out the form, hand over 3000B and a few pics, farang co-signs guarantee as "sponsor" and 2 days later you have the visa
On arrival to pick up the visa you must have confirmed and paid flights
Its easier than us Europeans going to Vietnam or America!
Of course the risk is all on the farang sponsor who signs the guarantee, but it seems the OP is a little too risk adverse to taking a chance on having a live in guy for sex on demand for 1-2 months :-)