Actually, if I recall correctly after only 5 years, your first sentence is correct. It doesn't matter how many symbols your alphabet has (i.e. base system used in application) because they can all be represented using binary. I don't recall anything about "optimum discernment" just that it is convenient to standardize proofs using a binary alphabet. For example, Huffman coding is proved using binary but it easily applies to ternary systems as well.
Apparently the optimum information-theoretic alphabet would have e (2.718...) bits, but it's a little awkward to work with a transcendental base. The pain in working with trinary circuits is why we use binary instead.
