A 1940 grammar book for American high school students says that the expression “back of the house” is “not good usage in an ordinary composition” but is “acceptable in conversation.”
He does not tell us what is “good usage in an ordinary composition.”
If the original comment is talking about sentences like #2 (e.g. “Back of the house stretched a fragrant pine forest, …”) then I agree that it is not good usage. However, I don’t think #2 would even be used conversationally in BrE, and #3 sounds impossible to me, so my opinions on these may not be very relevant to AmE usage.
I would have thought that both of these were wrong but if two native speakers say that they are “good” or even “acceptable” grammar, then I can’t argue with that!
Isn’t #3 in need of a definite article before the word “back”? Perhaps that would make it more acceptable in British English?
“In the back of Dr. Wingate’s house stretched a fragrant pine forest” is grammatically correct but nonsensical: it means the forest is growing inside the house. “At the back of Dr. Wingate’s house stretched a fragrant pine forest” is better, but for me there is still a slight awkardness about the combination “at” and “stretched”. Normally (in BrE) one would say “Behind Dr. Wingate’s house…”.
I agree with Dozy - For me, “In the back of my house” implies a back room or back porch, while “In back of my house” is the backyard or whatever else is back there.