She is not that Li clan. At all. She has nothing to do with it.
If I'm wrong, please provide a quote from Yrsillar.
Edit: Okay, after doing my own research I'm seeing where this is coming from and I actually kind of hate Yrsillar a bit now. Li Suyin's art comes from her mother's side of the family. Her father's family name is Li, not her mother's. One of the things indicated in a recent chapter is that her flesh sculpting art may have originated from the dead comital Li clan. If you're going to make a character named Li Suyin have a meaningful connection to the Li clan just make her explicitly descended from them through the obvious connection. Going out of your way to specify that her Li clan is not that Li clan only to turn around and say 'sike they actually are connected somehow' is lame.
Sorry for being so abrupt with you in my initial post, but I'll note that even with this new information I'd overlooked we've got no confirmation of a blood connection, and even if there was it's probably not enough to get her recognized as the legal heir to those lands. You can get your hands on arts without being family of the creator of said arts, especially if the creators are too dead to stop you.
okay but there are a few reasons, in story, for this to have happened.
First of all,
everyone hated the Li Clan. They were a "medicinal" clan with the flesh-sculpting Arts that filled the Hui fleshmarkets with things that wouldn't otherwise be possible. Individual Li could perhaps be redeemable, but the only clan that "liked" the Li were the Hui. And the Li were wiped out as Counts because the Hui refused to lift a finger to help them against Ogodei when he kicked off his invasion by assassinating the Li Patriarch.
The old Li lands are
heavily corrupted, and no Li has been able to gather power enough to attempt
any degree of reclamation. Not that any of the contemporary Counts would tolerate someone from the main Li house attempting to return to power anyway. No. Instead you have small amounts of Li blood by marriage within the Wang and Diao courts that are arguing over the claim. These Counts would be able to clear out the corrupted halls of the Li, but neither would be guaranteed the spoils afterwards which means that the Li Mountain has been festering for hundreds of years. The one with the strongest claim was the late wife of Sect Head Yuan He, who was a Li. She never pressed her claim, and they had no children.
So you have Li Suyin's ancestor (forget if they're Grandfather or Great Grandfather) who had his Dantian shattered for unspecified crimes, passing his Arts (which are almost certainly Li Fleshcrafting Arts) onto Li Suyin as she goes off to Cultivation school. He has long forsaken the Li name, either because he was a Li married off, a Li outcast, had married
into the Li and learned their Arts from his wife, or some other reason (like the Li being a deeply despised clan that would make rebuilding harder rather than easier).
Li Suyin's mom finds a successful commoner-cultivator that works at the Ministries for a husband, and he happens to have the last name Li. From the ancestor's perspective, this lets his descendants reclaim the Li name while laundering the baggage/scars, and he approves of the marriage.
now the Fleshcrafting Arts that Li Suyin showed us way back when were significantly too-advanced for her to fully understand. When she used the basics of them on Huang Da it freaked her out and I don't think Ling Qi knows how much she's studied them since. Because she's willing to support Su Ling despite disagreeing, I suspect she's willing to use the Li Arts for purposes such as: more easily testing on herself, confident she can repair any damage done.
Anyway, this brings things back to this Diao.
Entirely possible that this all has
nothing to do with anything this Diao has to say, and may be completely unused as plot points. I think that'd be unfortunate since it lines up so nicely with other thematic and narrative elements, but who knows how much the Diao know about the descendants of the Li
or how strong Li Suyin's claim would be.
We've known for a long time that Li Suyin had
Li Arts from her mom's side. The interaction where she talked to us about those Arts was pretty early into Forge, so it's not like this is a twist. In fact, that confession was around the time Li Suyin wasn't sure she should continue to be a cultivator, because it wasn't anything like the heroic Immortals she thought it'd be. And the Arts kinda, made her second guess the idea that being an Immortal was a good thing because she looked into the Li and. Ooof.
Anyway. This hypothetical storyline would
have to confront the question of whether or not Li Suyin is reclaiming the Li Clan Legacy or whether she's starting a new Li Clan Legacy and she just happens to have
some blood from that
other Li. A Li clan that will
not be honored as if they're the same Li as the clan of her Father. Because that's a persistent question in this world. How much can an Individual separate themselves from all the ties that bind them, and how do you draw the lines between connection and separation, those Boundaries.