Probably doesn’t matter one way or another. They’re not looking that deep - they have little time.
If it’s on the transcript and some scores are listed, then they’ll know the others weren’t good.
I’d either list all or none.
I don’t think it will impact admission either way. They’re looking at the class grades moreso - and scores can be reported later.
You are overthinking the impact of the AP scores. Report the 4’s and if there is room on the UC application after all significant EC’s/awards are detailed, then you can list the AP scholar. As I stated above, an applicant will not be accepted or denied based on a few AP scores. UC’s put much more emphasis on the class grade vs the scores.
Going to be blunt: Thousands of high school students, from across the country, who have taken the AP tests, are applying to the UC’s and have the “AP Scholar with distinction” Awards. It does not distinguish your student any more from all of the other students, who have exceptional test scores and are applying to the UC’s. A number of those students have perfect scores.
Indeed, “AP scholar with distinction” may be more related to the availability of (decent quality) AP courses to the student, while AP scores in relation to grades in the related AP courses may say more about how well the AP courses are taught than anything else.
Agreed… my son had the plain vanilla “AP Scholar” because the maximum number of AP courses that he could take before senior year was less than five. (He was able to take one in sophomore year, two in junior year.) He did report the award on his college applications because it was the only “award” he could remember earning in high school. It seems that neither of my kids are into the sort of activities that result in “awards” 
This is a great illustration of why AP awards aren’t highly regarded by colleges.
The vast majority of applicants are not targeting just one or two campuses. They are putting together an application for all of the UCs. Since the majority of UCs don’t consider AP scores in their admissions process, I can’t see anyone scrutinizing the fact that someone received an AP award, yet didn’t list all of their APs. There could be all sorts of reasons that a student chose not to list all of their scores. Maybe they are only listing the APs for the GEs that they want credit for. Maybe they only include APs in their area of study. Maybe they read that the UCs were test blind so didn’t include them.
Again, it is just my opinion, but I don’t see a UC admissions reader trying to “catch” someone or spend time analyzing why certain AP scores are missing. Over and over they say, “We don’t know what you don’t tell us.” Instead of worrying about what scores to send, use every possible space on the application to tell them who you are, what interests you, and why they should accept you.
OP, if your student does include the AP award in their A&A section, they will have an opportunity to describe the award, what was required and what they did to earn/achieve that award. They can state something such as they challenged themselves to take a rigorous course load in high school. They don’t need to mention why some scores are on the application and others aren’t.
I personally think awards in general have little meaning. There are exceptions of course.
But in general, what did someone do to earn the award - that’s what matters.
If you took 5 APs and got 3s on all of them, you get the award. That’s the accomplishment behind the award - but in this case you wouldn’t share.
No one gets an award for walking dogs, taking care of their sister, or working at Baskin Robins.
Awards are great - but Honor Society or best student mean little. The reason you got them - that’s what matters.
At least that’s how I see it.
The UC Activities and Awards section asks students to list up to 20 of the following. All extracurricular activities are valued equally, including non traditional activities.
Applicants are given 350 characters (over twice what is allowed on the Common App) to describe what they did, what role they held and what they gained from the experience.