Why doesn't nitrogen diffuse into blood?
I like it that nitrogen came to your mind ;) 

I guess in school they didn't tell you about the nitrogen at all, for the matter of simplification, because it is of no function in the body and the $O_{2}$ and $CO_{2}$ are the important gasses for biological function of breathing.

However, all of these small gas molecules are very small and generally the biological membrane is very permeable to them. That's why the cell cannot decide to let $O_{2}$ and $CO_{2}$ in and $N_{2}$ not as you suggest. 

(However, the cell is able to control the permeability of these gases to some content, based on the level of cholesterol in its membrane$^1$)

The process of gas exchange is generally passive. In alveolar membrane the gas flows from the site of its higher concentration (in case of gases we talk rather about partial pressure) to the site of lower concentration. The speed of this process depends mostly on the difference in partial pressures and if you let the blood "interact" with the air in alveoles for long enough, partial pressure of all small gas molecules would come almost to equilibrium. (This happens under physiological conditions for all of the three mentioned gases)

Khan academy is right too actually. This is because as $N_{2}$ isn't either produced or consumed in the body, its partial pressure in the venous blood is similar to that in the alveolar air, and there is no force to cause its movement between these two compartments in general. 



In the table you can see, that the partial pressure of nitrogen in the blood is the same as in the alveolar gas. 

Picture source