You would probably want to conceal that you're a college-educated American if you're masquerading as a member of a foreign faction. That this is not particularly well done is one of the interesting things about the ransom note.
There is some reason that Patsy met the police unshowered (as she tells us), in makeup and wearing her murder clothes while John was showered and shaved. There was no reason they had to call the police at 5:52 am. They could have called at 6 am, giving her time to remove her makeup and jump in the shower. That this didn't happen shows that they weren't in it together. No doubt Patsy was fussing with her note and lost track of time. Once John's up, it's too late for her to undress and shower.
If the crime had been planned for that night, the note would have been ready to go. It seems that there were nine plus one pages of false starts, indicating it was written on the fly, but it also has elements that suggest it had been given some thought before that evening: the line from Ruthless People, the amount of the ransom demand, the misspellings that refer to John's trouble with double ss's, various "Johnisms" such as and hence, proper burial and the "percenting"; the ironic mention of John's affinity for things southern (surely it's northerners who are known for their common sense, southerners for their charm), the reference to John's Atlanta Fat Cats, the ostentatious use of SBTC from the Bible that Patsy assured the police only John reads--and, of course, the movie references.
Patsy did the crime, staging and the note by herself as noted above, but the note is very complex. I can't for the life of me call to mind anything my family habitually says except that my daughter for years had the annoying habit of saying "Question?" before she would ask a question. It's easy to call to mind things people say that annoy us and Patsy was probably pretty annoyed by John. She no doubt ground her teeth every time he talked in percents. That one would have been easy. But all of it together? That must have taken some study.
So John's being fitted up for this murder, and it's important that he doesn't realize it until it's too late for him to do anything about it. But John's smart and figured out the basics of it that morning.
If Patsy thought that John was about to divorce her, she would know that her physical abuse of JonBenet would come to light. That could result in prison. It would undoubtedly affect a divorce settlement. Patsy would be disgraced and destitute. (There is one other piece of evidence, an odd little bit of staging, that increases the likelihood that this was on Patsy's mind. It's publicly known, but not discussed. I'm not going to discuss it here either.)