LOL, so your offer of proof is some dolt that is no more invested in the show than any of us, and has a gripe similar to you. The fact someone has given him a column is no more relevant than any blow hard sports columnist with an opinion. I can assure you that if I search, I can find other columns written by other people who happen to disagree with the link you provided.
For starters the whole thing wasn't an elaborate scheme from the get go, and that is the part your columnist got wrong, so any argument built on that assumption is also wrong. It wasn't until the last episode that Sansa started to put things together. The tensions between the sisters was real, until they came together and decided to take down a common foe. The thought that they had been conspiring the whole time is nonsensical, as to what would be the point of the scenes of the two of them together in private leading up to this episode be?
Your consistently crying about a lack of any proof. How much proof was needed during Ned's trial? During Tyrion's? did you expect Sansa to roll out the video tape and have Qyburn produce some DNA evidence? I have already explained the fact that it wold be fairly easy for the Sisters and Bran to provide all the proof they needed to convince the lords LF was guilty, the fact they didn't do so was because LF admitted his guilt. That doesn't mean they didn't have proof, only that it was no longer necessary to provide it after the confession.
When confronted with this explanation, your response is " Well bad writing....blah blah blah, the writers should have shown us the girls gathering the proof". Well then, had they chosen to do that, they would not have been able to setup the scene as they did, with the plot twist that it was LF on trial, and not Arya. Sorry, but that would have been boring as hell.
Lastly, you think LF should have not confessed, rather demanded to see the proof, denying the allegations to the bitter end. I'm not quite sure what you seem to think this would have accomplished, as it's quite obvious the burden of proof is considerable less in the midevil storyline than it is today in a court of law. LF made a quick assessment of the situation at hand, and determined (and rightfully so) that his best course of action for survival was not to deny the allegations, but rather to beg for mercy and somehow justify his actions by saying he did it all for Sansa. He knew his goose was cooked, he incorrectly made an assumption that Sansa was back under his control, and he thought things were proceeding exactly as he had planned. He was overconfident and careless, and it cost him his life.