How come that one's arm has to be at heart level so that the blood pressure can be measured accurately. I've tried researching this question, but most answers to it were just "if the arm is above the heart level the blood pressure is too high and vise versa," but I want to know why this is so.
This page (and many others) explain the idea rather well. This is more of a physics than a biology question, but the fundamental concepts are the same.
In fact, contrary to what you wrote in the question, the measured blood pressure should be lower than expected if the arm is elevated above heart level.
When you reduce the pressure on the bent pipe, the water level on the side where the pressure is reduced rises.
Similarly, When the arm is elevated, it is equivalent to the right hand side of the image, where the right hand tube's water level is higher than the left hand side. Raising the arm above heart level, with the pressure of blood at the heart level remaining constant, will result in a lower pressure being measured, due to the heart effectively having to pump the blood up the distance.
For the same reason, giraffes have very high blood pressures (double that of humans) due to their long necks. If their blood pressure was at the level of humans, they would faint when raising their necks, due to the blood pressure falling to zero at their brains.