Crimey crime crime -- you rascal you. You pulled a Whaleshark -- for this example is the same type of one I would have given, if requesting consideration for all possibilities.
Stellar, it is...that child's words brought tears to my eyes. I have paused for a moment.
The thing is, though, that child is gifted and talented, mature beyond her years, with heavy exposure to music, opera, classic literature and poetry, and possesses an uncommon ability to write better than most adults.
However, it does also mean that it is possible for a young child with similar sophisticated writing abilities, to have written the ransom note.
So I am willing to concede part of the point of 'completely ruling Burke out' as the writer of the note - for if I told docg to consider not ruling Burke out in this crime, then I cannot completely rule Burke out as the writer of the RN either, can I?
But, we would need to know for sure his full mental abilities at the time, knowledge/education level, his interest and exposure to culture, literature, and verbal level of sophistication, as well as all the info he would have needed to know for the note - whether he knew the adult Ramsey inside jokes, used the same manner of speaking, and the level of his spelling/verbal/grammar abilities.
He would also had to have had the same vocabulary level and known linguistics that Patsy/John used in their writings, and those which are used in the ransom note: hence, gentlemen, attache, fat cats, etc. Also, to know that he was exposed to, and remembered, all the lines in those movies-including the older Dirty Harry one(s), and employed them with the sophistication level of the vocabulary in the note.
The note is not only dramatized and gimmicky, but also well-educated with the proper (and aged/formal) use of the English language...
And, his handwriting would have to have not been ruled out.
This is why I usually rule out Burke, and any average teenager, as the writer of the note. However, point taken -- it is possible, per your example, that it could have been written by him -- but not probable, unless all those characteristics above were proven true for Burke....