You got the basic idea across, which is a big deal.
Though whether it's A or B isn't clear:
A) "this isn't all of the utility function, but its everything that's relevant to making decisions about this right now". ^U doesn't have to be U, or even a good approximation in every situation - just (good enough) in the situations we use it.
Building a building? A desire for things to not fall on people's heads becomes relevant (and knowledge of how to do that).
Writing a program that writes programs? It'd be nice if it didn't produce malware.
Both desires usually exist - and usually aren't relevant. Models of utility for most situations won't include them.
B) The cost of computing the utility function more exactly in the case exceeds the (expected) gains.