Weight. On warships an allowance is often given to an increased weight of paint over the ship's life, which can be significant enough to affect calculations. For an aircraft that's obviously less acceptable.

Paint is surprisingly heavy.

For reference, the paint on a 747-400 will weigh over 250kg.

http://www.boeing.com/commercial/aeromagazine/aero_05/texton...

If the ship was unpainted steel, perhaps the overpainting would draw excess attention, like wearing a mask in public might?

Like this 314: https://jpbpa2.files.wordpress.com/2015/02/new-image.jpg

I thought it wasn't the weight so much as it was the Pan-Am markings.

I believe it was because they were going to be flying through a war zone and did not want the US and Pan Am insignia on the planes. Of course, it actually helped them when they flew into the Dutch port as the Dutch flighters saw the US flag and backed off.