Saddle height is important,
Saddle height is important, but it is not the only thing that can have an effect on your knees.
For most people the saddle is at the right height when you can sit on it with the pedal at the lowest point of the stroke and your knee is slightly bent. This gives the optimum combination of comfort and leverage. That said, if your ride involves climbing a lot of hills you might want to drop your saddle a nudge though.
Moving the saddle backwards or forwards is going to affect your reach for the handlebars more than you’re pedalling, but we are all different so I could imagine a scenario where if you had short legs and the saddle was too far back you weren’t getting as much power behind the pedal – which could hurt your knees. Basically if you feel like you’re stretching for the pedals your saddle is in the wrong place.
The other thing that can develop the muscles in your knees though is pushing a big gear ideally you want to be turning the gears fairly easily – if you have to push or stretch – the gear is too big. If you are riding fixed – controlling the bike using the pedals is going to bump up your muscles too.