Rudy Guede had a serious problem. Clear physical evidence linked him to the murdered victim.
The stories he told to try and explain the evidence give us a clue as to what really happened. Rudy claimed to have been on toilet when a stranger bust through the door, that he fought with the stranger in the kitchen. The fight probably did start in that area, but it was with Meredith. She came home while Rudy was using the toilet. He didn't flush to avoid alerting Meredith to his presence, then tried to sneak out the front door. What Rudy didn't know is that the latch on that door was broken. Meredith would have locked the deadbolt to keep it from blowing open.
Rudy looks for another way out, but runs into Meredith. A short but brutal fight follows, moving into her bedroom. Rudy pulls out a knife and kills the poor girl.
Rudy has blood on his pants and other clothing, his hands are a mess. He goes into the small bathroom to clean up. He takes his shoes off and attempts to rinse the blood from his pants. The footprint on the bath at is from the diluted blood flowing down his leg. Rudy puts his shoes back on and returns to the murder room. He needs Meredith's keys to open the front door. He takes her money, credit card, cell phone and a sweatshirt to cover his bloody shirt. While doing so, he steps in the pooling blood. He locks the bedroom door on his way out, but doesn't lock the front door. He does not want to be seen standing outside the cottage fumbling with keys.
Rudy heads home by a route outside the city walls. Avoiding the basketball courts were he is likely to encounter people that know him. He tries the side gate near his home, but finds it locked. He continues on the path to the next gate, when one of the cell phones gets an incoming message. Realizing the phones link him directly to the dead girl, Rudy tosses them over a wall into what looks like a ravine before continuing home.
I recognize the theory about the route taken by Guede as coming straight from the True Justice website. Wasn't it Kermit that produced a powerpoint of that theory?