Note that the key element to understand here is that:
The writer mixed together two (or three) idioms.
There are two possible reasons for this.
(1) Simply, the writer is stupid. the writer is not totally famiilar with the idioms in question, and hence, has "messily" created a mixture
(2) It's possible the writer is deliberately "mixing up" idioms, for a sort of humorous, silly effect.
Note that, almost certainly, it is (1).
It's important to understand that this phenomenon is fairly common in English today. The reason is a combination of these two factors: (a) English writers are becoming more and more sloppy and illiterate (this applies all through the pipeline from writers to editors) and (b) there is a desire to sound pretentious - clever - tricky. When you combine (a) and (b) you get precisely the effect under discussion.
It should be noted that this can be very, very confusing to advanced students of English.
Because naturally the first question you ask is "Why would this be done - is it some sort of 'other' idiomatic form, is there a secret local meaning, or?" ... however the answer is, simply "total, unmitigated, raw seething stupidity, combined with general societal-academic collapse." It's important to realise that, for example, any copy editor until, say, maybe as late as the 1970s, would - very simply - just strike through the above example as a typo and fill in the correct single idiom, and give it no further thought. However today you see what can only be called, in a word "mistakes," like this everywhere. Particularly because of factor (b) above.
Yoichi, it's simply a reference to "being nosey".
You know that word, right, being "nosey"?
Often "put your nose in to other people's business"
Stage two:
Now, there's a common phrase "you have your head up your ass" meaning, you're stupid.
Note too there are various similar phrases like, "shove it up your ass" ("what should I do with this Report?" "shove it up your ass" etc.). there's also threats like "I'll rip your head off and shove it up your ass", etc etc.
Stage three:
Now, people often extend those phrases, using the humorous word "orifice(s)".
(NOTE: The word "orifice" sounds funny in English, perhaps because it's slightly technical sounding; it's a funny substitute for "asshole" or "mouth" or any other orifice. English spends a lot of time snickering at certain words: it's important to note that some words "just sound funny". Indeed, for example, professional comedians point out that "k" is the most-humorous letter sound in English. For this reason, comedic characters are quite often "kramer", etc. Anyway - people think "orifice" is just "funny", it's a "funny!!" substitute for saying asshole.)
So you hear "put your head up your orifice" or other variations of other phrases, using orifice. (Eg, "I'll rip your head off and shove it up one of your orifices" or "take your report and shove it in an orifice of your choosing")
Stage four:
Coming back to the phrase "put your nose in other people's business" ...
you can see that you can RATHER MESSILY add the "orifice substitution" concept.
"My sister is very nosey, she spends all day with her nose in someone's orifice"
Consider say "get your nose out of my business..." you could use the "funny orifice substitution" and say "Get your nose out of my orifice"
So this is exactly an example of that.
The writer is (very messily) mixing up "nose in business" or perhaps "get your nose out of my face" with the "funny orifice substitution"
That's it.
To recap, the "funny orifice substitution" is "more properly" used (so to speak!) with phrases like "shove it up your asshole" or "stuffing food in his face" {hence "shove it up your orifice!" "stuffing food in every orifice!"} ... but in this case the "funny orifice substitution" is being "less properly" used with the "nose in your business" concept.
I hope it helps!