I’m always tempted to pronounce ‘bún đặc biệt’ (boon dahk bee-et) as ‘boondock beet’.
I’m voting for “out in” because the “boondocks” refers to a remote location, which would be well outside an urban, suburban or even small town area.
When you’re out in the boonies, how far is it to the back of beyond?
Farther than that.
It is possible to be out in the boondocks and down in the dumps simultaneously. In fact, being out in the boondocks could be the cause for being down in the dumps.
IMHO, both phrases are correct but they carry subtly different connotations. “Out in the boondocks” is relatively neutral, while I think “down in the boondocks” suggests a certain amount of disdain for a lower class of existence.