From the amount you struck out, I believe you realized that my response was not
so ill considered as all that.
About the paper airplanes, I'm painfully aware that space is so alien to my experience that any intuition needs to be backed up by calculation. But I note that the ISS is about 60 m long and the airplane is 8 cm long. That is a 750-fold difference in length. Let's leave out differences in materials and shape. That makes the cross-sectional area (and therefore drag) of the space station be 7502 times the airplane. The mass of the space station is 7503 times the airplane. The resulting acceleration due to drag on the space station is 1/750'th what it is for the airplane. So 6 months for the plane to come down is the same as centuries for the space station.
I can believe that.
Edit: Missed a factor of 10 on a calculation, fixed. Also added explanation of why the effect of drag on time to hit Earth scales linearly with length. Please note that the linear scaling is for the same shape and materials. The space station has a different shape and materials than the airplane. In particular the space station is hollow. Thus it will probably come down much faster than naive scaling up of the airplane would suggest.