You're point is extremely well put. Rationally, he would not make deliberately incorrect statements if he really wanted "credit" for the crime. Only thing I can think of...he's now quite confused and is acting as more than one personality, or has severe memory problems or something. The multiple personality thing has been mentioned as a possibility.
I'm thinking too hard about it....and it likely isn't that hard.
Karr has a grudge against power and the money. His life has been a flop.
Being from the south, Ramsey would be in the southern papers more than here...up north.
There's some connection to the Ramseys but we don't know how yet.
From Sandrock (or whatever his name is) we learned that it appears that Karr was familiar with Colorado....but that might just be by doing web searches......except he knew the color and position of the newspaper building that the writer was from...by heart. Is that toooo familiar? Had he been there looking at Victorian Houses? Had he worked on any? There are a lot of guys who work for subcontractors doing work under the table.
I think John Ramsey said that the little room where they found Jonbenet had been painted shut. Who was the painter...and how long ago??
He's not THAT confused. He said after checking that the record light was on (the flitting eyes) that: it was "an accident" and then continued "That would make it 2nd degree murder not 1st degree".