That's something I've not heard before. Could you give an example or two?
The first thing that made me think of it were the words "and hence." Both of my Mexican correspondents have used that phrase; in Spanish, it is "y por lo tanto." It's grammatic and idiomatic in Spanish; a Spanish speaker would not leave out the word "and" since it is part of the idiom (I think! it's a long time since I spoke Spanish regularly).
Then there was the sentence at the beginning: "We are a group of individuals that represent a small foreign faction." That has the sort of rhythm and flow that Spanish has. Spanish is a very ornate and flowing language compared to English. In Spanish, I think it would be "Somos un grupo de individuos que representen una pequeña facción extranjera." (my Spanish is not great, so this may not be accurate)
The very next sentence has a spelling error in it: "We respect your bussiness but not the country that it serves." That stood out because the rules about single "s" and double "ss" are often unclear to Spanish speakers. I can't recall off-hand any words with double "ss" in Spanish in the same way there are in English.
In English, I think the sentence would be more like "we respect your business but not the country that you serve." While you can say that a business serves a country, it's not quite right. In Spanish, though, "the country it serves" is grammatically and (I think) idiomatically correct. Unlike English, Spanish does have a third person gender-neutral pronoun.
Then comes this sentence: "Make sure that you bring an adequate size attache to the bank." It's awkward in English, that's not how an idiomatic English speaker phrases an idea like that. An idiomatic English speaker would say something like "be sure to take a large enough briefcase to the bank." The word choice, the order of the words, it's correct but not usual.
In Spanish, though, it goes "Asegúrese que usted trae un tamaño adecuado attache al banco." Again, keep in mind my Spanish is old, rusty and quite lousy--but I think this is it. It goes directly into English as "Make sure that you bring an adequately sized attache to the bank." Sound familiar? And, unless I'm really way off on my translation, that's the way an idiomatic Spanish speaker would choose to address someone formally.
This sentence: "If we monitor you getting the money early, we might call you early to arrange an earlier delivery of the money and hence a earlier delivery (the word delivery is crossed out) pickup of your daughter." An idiomatic English speaker would understand that the word delivery works in both places: someone (John?) would deliver the money, the kidnappers would deliver JonBenet. I think an idiomatic English speaker would deliberately use the word "deliver" twice to emphasise the symmetry of the two actions: money for daughter.
The word delivery would not work for delivering JonBenet in Spanish, though. I think the implications attached to the word delivery are wrong for Spanish. I'm not sure, though; it has been too long since I last spoke much Spanish.
I think there are other examples but I'm hitting the wall on idiomatic (rather than merely grammatically correct) Spanish. And my old dictionary is getting more of a work out than it's had in over 40 years, so it may not be up to date at all. Just like English, idiomatic Spanish changes over time, new words are added, other words become old fashioned and rarely used, etc.
If there is something to my idea, then I see two possibilities: a) someone who thinks in Spanish and is fluent but not idiomatic in English wrote the note; or b) someone who has a lot of contact with a person or persons who think in Spanish and are fluent but not idiomatic in English was imitating their manner of writing/speech.
My Spanish is not good enough to be considered in any way reliable. I've lost most of the vocabulary and I'm no long idiomatic. I doubt this is worth enough for anyone to spend money to pursue it but if someone knows a Spanish speaker who has good but not perfect English, it might be worth it to do a little testing. Actually, two Spanish speakers. Have one translate the note into idiomatic Spanish, then the other translate back into English and see what you get.
I want to emphasise again, I am not a linguist and not even a fluent or idiomatic Spanish speaker. An expert might not agree with any of this at all.
Now my own English is all mixed up! My Spanish is trying to come back and it's getting the language centers of my brain all confused.