Seems to me like the Queen was entirely in the right
The public treated Diana like she belonged to them, and it killer her. Then they continued to act like she belonged to them when dead. There's even a clip in the movie of a woman at a public gathering weeping about "why couldn't we leave her alone?" whilst not leaving her alone.
Issues like the flag not at half mast really illustrate how the public seems to think the royal family exist to play out dramas for their amusement. If you want to be rid of the monarchy, fine, but if you want to keep it, don't insist that the common man has the right to override the traditions and rituals that constitute that monarchy. Most of all, don't pretend you own these people.