Earlier quoted context omitted.
I get where your coming from, but many people can get all the individual concepts and still not make the connection. If they want to double X, they are happy to use X + X, 2 * X, or X It's probably a learnable skill, but it's just not directly part of CS classes. Someone can learn X XOR 1 is the same as X MOD 2, it's another to use XOR when they can't recall the MOD symbol.
Maybe I'm missing something but in your two examples, what you refer to as skill is just recall. I would argue that in the context of alternative solutions, the skill would be knowing when a better alternative is needed when it isn't immediately obvious. If I knew mod wasn't available yet I neded an analogous operation finding an alternative is trivial even if I don't recall it. I wouldn't call that a skill.
For a non programming example, you can use the handle of a shovel as a long stick. This should be more or less obvious when looking at a shovel, but I have seen people ignore shovels when looking for a stick to do something.