Got any source for that? Closest I can find is a Polish cryptologist facetiously adding "Heil Hitler!" to ENIGMA encrypted messages he sent to Britain.
"we relied on the fact that the greater number of messages began with the letters ANX—German for "to", followed by X as a spacer"
http://en.wikipedia.org/wiki/Cryptanalysis_of_the_Enigma
Compressed files (indeed ANY files) having predictable headers is, of course, a major problem, and the argument that you could just omit the common stuff won't work very well either. (Let's suppose you leave off all the static parts until you get to a length stamp -- lengths are a classic example of not-very-random numbers (more significant digits are prone to be lower-valued).
In general, you want your cryptographic system to be reasonably foolproof when used by bored, careless people. For this reason rolling compression and encryption into a single implementation is probably the best option.