With all respect, though, Karl and Wharton -- you cannot guarantee that the organisations will be so cooperative as in your scenario. It's not scaremongering to say that, in reality, there is no idea how the negotiations will go or how smooth they will be. It's just common sense. You might expect that the EU/ NATO/ remainder of UK would be keen on making things smooth and pretending that Scotland were not independent and still part of the UK. But it's not much more than hope, really.
There are, after all, things that a united UK can bring to the table that a divided UK just doesn't. Aside from anything else, you can easily imagine that in the EU, Scotland might be keen on promoting its native language, which while as yet unmentioned could potentially lead to a need for Scots Gaelic official documents, a whole new layer of bureaucracy, etc. You'd hope that the new Scottish government doesn't try to be so stupid as to demand documents in Gaelic, but if it did it would lead to the negotiations at the very least dragging out far longer than has been suggested.
When it comes to NATO, it's not clear what an independent Scotland offers to NATO at all. A hopelessly under-budget armed forces, no Nuclear weapons, rapid removal of Trident from the current bases... these aren't just things that will be tossed aside as not important by the rest of the NATO members. And so, again, there is no guarantee that the transition will be quick and easy, and that Scotland will get all it wants (or even most of it) out of the negotiations that will inevitably follow.
I don't see this as scaremongering at all. It is surely obvious that what follows a Yes vote is a period of major uncertainty. Of chopping and changing. Indeed, if the Scotland's Future paper is to be believed, of Scotland trying desperately to have its cake and eat it. Let's keep the pound, the EU/ Nato terms and exemptions negotiated for us so carefully by those nasty people at Westminster. Let's have everything we would have had if we'd gone for Devo-max, in other words, only now with a lot more hassle and rather fewer guarantees that it will happen after all.
A bit more realism, and a bit less of the insults and protestations and general smear campaign from the Yes camp, and they might just look a bit credible. As it is, the Yes vote is an unrealistic Utopia that will only work if Scotland gets absolutely everything it asks for and everyone else decides that having two smaller countries to deal with is preferable to having one large and strong one. No-one knows, properly, what will follow Independence. Except that it will be messy. And, in implying that it will be easy, the Yes campaign is lying through its teeth and knows it.