What are you going to pad it with? Random values? In that case, I'll just make two requests for the same information and clip it where they differ. Some sort of value based on the message? That also has issues, see link below. So far it doesn't seem like there are any obvious crypto ideas that are not also wrong.
So, byte 0? You're not really using ECB, are you?
At least I can point to it as another example of someone not expert in the field making a stupid statement about crypto...
I think the general problem of padding with random values resulting in non-determinism would still matter in some cases, but IANAC.
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.
Incidentally, it's also clear that if the encryption schema is large relative to the compressed data then it will also be harder to decrypt (of course if the encryption schema is public, e.g. a public key, then this is decidedly not true).
So, none of this should be terribly surprising. What it does suggest is that you should compress data before (or while) encrypting it, and the better your compression algorithm, the more entropy there will be in your data, and the more secure your encryption.