I assert that an "unrecognizable encrypted message" will be a random sequence of bits. Is my assertion correct?
It's neither correct or incorrect because the specific notion of randomness hasn't been specified. Your statement is falsifiable, however, since sometimes a non-random string of bits is what you want to get out, if what you would expect to get out normally was also non-random. And you want them to be non-random in the same way.
Should I be using the phrase "high entropy" instead of "random"?
No. This was the notion of random I pointed out that didn't work. If you add 16 zeros to the front of a gigabit random message, that's pretty recogizable, even though the entropy is may be very close to maximum.
Of course, this assumes there is no other way to detect a hidden message besides reversing the stego process and testing the result.
Don't count on it. Statistical tests can find correlations you hadn't suspected were there. In fact, for some message types, _not_ finding the correlations may indicate dithering, or maybe a steganographic message.
property 3) the reverse stego process should product frequent "false hits". In other words, the reverse stego process should frequently produce high entropy bit sequences, even if there is no hidden message.
If the prior probabilities of the message type that you're hiding in are not random, the steganographic extraction shouldn't be either, because then there's a distinction between an unaltered container and an incoded one. Eric