Indeed but CGPGrey explains it in excruciating detail on YouTube. https://m.youtube.com/watch?v=qD6bPNZRRbQ
Actual question still sticks: Takeoff on 18 southwards basically makes you follow the river immediately. Where did this guy encounter his left/right decision, to get back towards white house? he must have made almost a uturn then?
And even assuming the article is a bit inaccurate and he took of northwards (thanks for pointing out the patterns pilots have to fly if doing that @ others): I still cannot imagine how that plane flew and where it matches the description of: "When I reached 1500 feet I looked down. I was crossing the river. It went right and left."
???