Author here. I'm sorry if you don't think my fill's accurate, but again, I'm only as good as the research I can find, and some of the pages I used as references (I posted a couple below, if you're interested) stated that a lying down insertion was certainly a viable one. If the authors of those seemingly reliable, scientific, medical tutorial articles are wrong, there's not much hope for one lone anon writing for a kinkmeme, of all things.

Considering that it's a fanfic for Sherlock, a show that consistently has fairly obvious medical inaccuracies (the one that comes first to mind being the belt stabbings in TSOT, but there were plenty of others as well), I wasn't too worried about being spot on about everything. Not to mention that, in BBC's canon, the idea of Sherlock having anorexia is pretty ridiculous; my portrayal of him alone is already going to be off because of that, so I'd assumed that if you could look past any OOCness? (I'm just going to say that's a real word, because I don't know how else to put it), you'd also be able to look past the smaller mistakes that really don't affect the story much.

I appreciate your opinion, but short of going to consult a doctor, there's not much else I can do. Sorry you've not enjoyed it. :/

http://www.healthline.com/health/nasogastric-intubation-and-feeding#Overview1
http://www.survivinggrays.com/how-to-insert-a-nasogastric-tube/