They aren't talking about NIE as just the number on a piece of paper as it doesn't prove residency. What they mean is Certificado de ciudadano de la UE (commonly known as NIE Verde or just NIE). All EU citizens living in Spain for over 3 months are legally required to have one. Non-EU should have a TIE.
NIE Verde is issued the same day IF the conditions are met (working for a Spanish company OR self employed in Spain OR proof of funds+private health insurance). TIE takes longer.
You need a NIE verde (if you're EU citizen) or TIE (if non EU) to prove your legal residence in Spain. You might be able to convince them to accept Empadronamiento instead but even that is not easy to get. No way around this requirement, they clearly say, to apply in Spain you have to be a resident there.
It depends on the local policy and your luck. I've heard of some people getting rejected in Laos with no refund. I personally know a guy who applied in Phnom Penh, they accepted his documents. When he came a week later to collect his passport he was told his visa is not approved. But they refunded him the fee and didn't put anything in his passport.
He applied and got his visa in Saigon a week later.
Vietnam (Saigon) was very easy except for the appointment thingy. The only thing they ask and some others don't are 6 months of bank transactions printout (as opposed to just the final balance or 1 month as in some other embassies). But I haven't heard of any rejections in Saigon yet.
Has been a report like that from Vientiane. Unverified.
There was also a report from someone I've met personally who was rejected in Phnom Penh a week after he applied. They refunded his money though and didn't put anything in his passport. He got the visa successfully a week later in Vietnam.
As Tod has mentioned most reports indicate that one should avoid the Embassy at KL. Go elsewhere - Indonesia, Vietnam etc. Some require an appointment.