Why did Death help set Ankh-Morpork on fire?

Question

At the way to work, I've been thinking about Death (the Discworld character, not the actual thing) and the rules it follows. I remembered a scene which makes him look like an obvious antagonist.

In the Colour of Magic, Twoflower explains concept of insurance to the owner of the Broken Drum, Broadman:

"Tavern fights are pretty common around here, I expect?"
"Oh, fairly."
"No doubt fixtures and fittings get damaged?"
"Fixt - oh, I see. You mean like benches and whatnot. Yes, I suppose so."
"That must be upsetting for the innkeepers."
"I’ve never really thought about it. I suppose it must be one of the risks of the job."
Twoflower regarded him thoughtfully.
"I might be able to help there." he said. "Risks are my business."

However all the owner understood was that “If my property gets damaged, I will receive money” as seen later on:

Down in the cellar Broadman looked up, muttered to himself, and carried on with his work. His entire spindlewinter's supply of candles had already been strewn on the floor, mixed with his store of kindling wood. Now he was attacking a barrel of lamp oil. "inn-sewer-ants" he muttered. Oil gushed out and swirled around his feet

He did not manage to set his property ablaze all by himself though - his tinderbox was damp. Which is what my question is about:

A lighted taper appeared in mid-air, right beside him.
Hᴇʀᴇ, ᴛᴀᴋᴇ ᴛʜɪs.
"Thanks," said Broadman.
Dᴏɴ'ᴛ ᴍᴇɴᴛɪᴏɴ ɪᴛ.

The Discworld wiki discards Death's role completely:

The Great Fire Of Ankh-Morpork was caused by Broadman the owner of the Broken Drum, when he tried to burn down the bulding

Is there any (in universe) explanation what Death's motives were here? I mean he clearly knew what is about to happen. Out of universe, it allowed for awesome dramatic scene of course:

Broadman went to throw the taper down the steps. His hand paused in mid-air. He looked at the taper, his brow furrowing. Then he turned around and held the taper up to illuminate the scene. It didn't shed much light, but it did give the darkness a shape...
"Oh, no" he breathed.
Bᴜᴛ ʏᴇs, said Death.

The closure of the scene also almost implies it wasn't Broadman who threw the torch.

Answer 1

Death happens to know when people are supposed to die. There is a preconceived reality (as shown in the book Mort) in which people die when they are supposed to. If they do not, this alters the reality of Discworld, which will then attempt to correct itself.

Therefore it's possible that the fire was supposed to be started, and would kill a number of people. If that didn't happen, and that large number of people who didn't die in the fire continued to live, this would distort reality greatly as they continued to exist.

Therefore it was Death's duty to ensure the fire was started. Simply because Broadman was unfortunate enough to be unable to complete the job himself, did not mean the fire didn't have to be started.

The fact that Death does not turn up for everyone

as seen later in the Colour of Magic, as Rincewind is perturbed by the fact Death sends a minion, as he feels he that Death should appear personally because he is a wizard

and yet he turned up for a simple barkeep, shows that something more important was happening than the death of a single unimportant person.

Answer 2

In The Colour of Magic, Death isn't like the Death we know and love in books like Mort or The Hogfather. He's a much darker and almost cruel being, apathetic to the lives of mortals, as seen when he pretty much randomly kills a fisherman by stopping his heart. So it's not as farfetched as you might think that Death himself would influence the outcome of a calamity.

It's also worth pointing out that during the events of Colour of Magic, Death was having a particularly bad day at work:

“Oh no, not -'
OF COURSE, WHAT'S SO BLOODY VEXING ABOUT THE WHOLE BUSINESS IS THAT I WAS EXPECTING TO MEET THEE IN PSEPHOPOLOLIS
'But that's five hundred miles away!'
YOU DON'T HAVE TO TELL ME, THE WHOLE SYSTEM'S GOT SCREWED UP AGAIN, I CAN SEE THAT. LOOK, THERE'S NO CHANCE OF YOU-?
Rincewind backed away, hands spread protectively in front of him...
'Not a chance!'
I COULD LEND YOU A VERY FAST HORSE.
'No!'
IT WON'T HURT A BIT.
'No!' Rincewind turned and ran. Death watched him go, and shrugged bitterly.”

The entire system of Death got muddled up and as a result people aren't dying correctly. Which of course means now Death has his work cut out trying to fix it all, especially since there's a particular Wizard refusing to keep his appointement.

If Rincewind had willingly opted to take a "Very Fast Horse" to Psephopololis, who knows, Death might have been in a more forgiving mood at the Tavern?

Answer 3

Death was not assisting in lighting the tavern on fire. Broadman was having a near Death experience. Death was just being polite in doing his job and it just "happens" that it results in the fire.

Death knows what the result will be and all that, but he's not allowed to interfere (at least not supposed to) and while he does know the result of those actions he generally tries to act/think as though he doesn't. So you have to disregard his knowledge and consider his actions as though they are coming from someone who is just doing their job and is a nice guy. He knows what is going to happen and how it all goes down, but his actions will always reflect him as a "you're going to react badly to his job, but this doesn't have to be a terrible experience" type personality and in that personality is the answer of why he gave Broadman the method to light the fire. He was just placating someone about to die.