Sorry to all for my less than informative and evidential posts last eve.
Anyway, now I do have some 'evidence' as to why I think that Gimli shouldn't have stood on the Tomb of Balin. I'll disregard the whole 'respect' thing as I don't know that much about movie Dwarven culture. Sure, Gimli spends a lot of time kneeling before the tomb, but then maybe all bets are off once the Dwarf's blood (if they have blood, which is another assumption) gets hot.
I'll be referring to the attached images. In 'Gimli,' we see the Dwarf atop the tomb. Aragorn and Legolas - archers - are in front, and Boromir stands out there as well with sword and shield. Gandalf and the hobbits stand off to the other side. Gimli2 shows this from the front - what the orcs will see when they enter the Chamber of Mazarbul. Gimli3 shows Gimli after the affray has gone on for a few minutes. The Dwarf is still atop the tomb. Aragorn has switched from bow to sword, and at this time everyone is engaged. Gimli has taken one or possibly two hacks at orcs, and now is dodging the troll's attack.
Okay, so for me, I would say that this 'come and get some' Dwarf would have been better positioned for battle directly in front of the tomb. You'll notice if you watch the scene that his 'count,' which becomes more important later, is slightly - if at all - above the individual hobbits. He could have been right behind Aragorn and Legolas, so that when they drop their bows he could add to the ground attack. But...
And now for the Seat of Denethor. In Gimli4, we can see the Dwarf happily planted on the black throne. Please look closely at his legs and his head in relationship to the throne. In Gimli5, we see that the Dwarf is so comfortable that he's lit up his pipe - hammer and tongs!
Now I will conjecture that all of this fuss about disrespect for the Seat of Denethor is for not. Why? Again, look at Gimli4. If that's a human-sized throne then I'll be a winged polar Balrog.
So, my conclusion? The Army of the Dead stole the real throne and replaced it with the one we see. You also will note that the King's throne also is missing.
No wonder they were in a hurry to leave on the Pellenor Fields - had to get out of town before Aragorn discovered their prank. Aragorn cares not as he sees the obvious fakery. How else can you explain it?