Your reasoning COULD be correct, but I can't be sure. However, I was told by a very nice agent at the 1K desk based in DTW that you can't always rely on breaking down segments -that is, even if YCC-LAX shows availability in F and LAX-MEL is available in C, you MAY not be able to confirm the flights all the way using the same XC booking. I am told that they are under different inventories or something.
*HighFlyah*
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"To Fly High, Fly and STAY *UNITED* - that's the only way to do it."