Where you went wrong, is that you were sitting up rather than lying down to watch television with some pillows gently propping you up. You just need to be lazier.
Seriously though, I bet the whole television setup was just an afterthought unless you were staying somewhere swanky. Or maybe they were just trying to avoid the glare through the big windows.
You're right about how important it is to consider the screen angle. I remember when big flat-screens first became a thing, we bought one and expected it to fit where our old television went since we'd measured everything. Foolishly, we only considered the length and width of the television. Our new T.V. technically fit fine there, but it was super uncomfortable to watch thanks to having to constantly look way up at it. We didn't think that one out too well.