Imagine being a Villa or Brentford fan in this scenario. When we were a mid-table side we used to complain a lot about having to wait until the middle or the end of the programme to see our highlights, even if we'd pulled off a pretty big scalp.
So yeah, you're a Villa fan or Brentford fan, high off the fact you've nicked points off one of the two most successful teams in the country (historically). You turn on Match of the Day expecting to be on first or second, but find out you've been bumped down the list because City beat Chelsea.
The big stories of the day were that United lost and Brentford nicked a point off Liverpool. City going to Chelsea and winning has happened quite a few times over the years -- enough for it to not really be that much of a story. You can say "the PL winners beat the CL winners, so we should be on first" all you want, but that doesn't mean anything to the vast majority of people watching.
Also I think us being a 12:30 KO has something to do with it. People have all day to learn the scoreline and find the highlights on YouTube, etc. whereas United lost between 3-5pm, Liverpool drew between 5-7.30pm, so MOTD could be "breaking" the story for quite a lot of people who won't have seen the goals or may have even missed the story.
And also, imagine being a United fan in this scenario. They lost today and they're on first, so the conclusion from their perspective is: "Of course we're on first because the anti-United BBC love to laugh at us whenever we drop points", etc. etc. The MOTD team don't take anything like this into consideration, they just organise the matches based on how much of a shock/story it is and plan from there.
City beating Chelsea was a shocking story to us but to everyone else (i.e. MOTD's audience) it's just one petrol club beating another.