Well it just makes more sense than anything in the precision tree. When you look at Sivir she isn't trying to trade through sheer Autos, she wants to do Poke/Burst with Q, so in some respect it's almost similar to a Miss Fortune except instead of having different ways of doing dmg / poke, Sivir has basically 1 main tool (W develops later) where she wants to poke you down low and then chase you down.
With DH and Coup De Grace you get that extra Bonus dmg so that when you do get ppl low it just does more and more dmg the later the game goes. Sivir doesn't have a problem getting ppl to low hp, she is pretty good with it; but unlike MF who's Bullet Time can be used to secure kills, sivir is trying to Run you down when you get low enough, getting DH makes more sense imo when you are trying to get kills on her.
If you are just playing to farm and jerk off then i mean i guess go Fleet
If you want kills tho then DH is the best way of getting those consistently.
PTA is not good on her, her autos are good but not great, she doesn't have a true Atk Spd buff (her R scaling Atk Spd % W isn't a on demand burst) like a Tristana or Kai'sa for Example, so you can't quickly proc PTA
Lethal Tempo is also poo in lane since your main dmg is Q, that means when you do hit your Q's you are procing LT but you aren't generally going in to use it until after the ppl are low; even when you are mid-late game LT is kinda un needed, it has like maybe 1 point where it is REALLY good and that's when you have 2 items but not the 3rd; Before then it's garbage and after the 3rd it goes down hill imo.
So now you have fleet which is just taken cause meh, the other 2 in precision are trash for her so fleet just makes her safer; personally i hate this rune on her cause it enables really passive play, Sivir is already pretty safe compared to other immobile ADC's and her Q is good but Fleet doesn't help her Win lane, only helps her to not Lose it (too dramatically anyways). It has occasional utility when it comes to chasing ppl down but I'd say it's actually just not good on Sivir and it's taken now because ppl don't know what else to take.
Sivir is more like a Mage early, she relies on her Q just like a Mage would rely on their main Dmg ability (Brand W for example), now in theory I could use Comet on Sivir since it would actually be good for poking and even the rest of the sorcery tree is actually (in theory) pretty good for her, she scales well with AD obv, she could use Manaflow band or Nimbus cloak well, but the problem isn't that, the problem is that the Rune only would help her with Poke and poke (in theory for her) would only be good in lane; as Sivir scales she relies more on All-in Running ppl down and Ricochet and even tho Q hits very hard her kit becomes more well rounded.
Getting things in the Domination tree give her similar things actually, for example I use Taste of Blood which is similar to Fleet although it has a condition of doing dmg to a Enemy. You can use Eyeball collection but personally i use Ghost Poro, gives some scaling but the overall utility in lane is the main reason; it helps a lot imo for avoiding ganks. The final tier also gives ways to upgrade her utility in some way, either more access to your Ulti or even more Healing on your Q (make no mistake, this heals for quite a bit through the duration of the game) and overall you are getting a similar sort of experience that you would if you were taking Fleet. However when you get CoupdeGrace and Triump the build really comes together, because as you do what Sivir does (Q poke) you will spike earlier, (often times I'm at 10+ stacks before 20minutes).
So when you look at the Build and combine with the Runes you get a Sivir who hits 1 item sooner (more dmg) while also having runes that enable her to use that 1 item spike to kill or setup kills more consistently and earlier while giving her more dmg scaling throughout the game.
I would say the 1st time I ever used this build i was like Dam this is really OP because you are so safe, you are hard to gank, you do good poke, good wave clear, decent all in early (not great by any means) but since you have DH/Coup that means your All in potential gets ramped up quite a bit, a champ that normally couldn't really all in can now to it and scale while doing it.
Even with that though I would still say she is only a little bit better this way. Honestly, Precision on her is pretty dog poo as a main rune and that's really the thing you should be focusing on..It's not so much "Why DH" but more like "why are ppl taking precision on her" when you really look at that question you get a better frame of why DH works with her Kit