When Vosen realizes Nicky's deceit he orders Desh to kill Nicky and Bourne after terminating Daniels. Landy is outraged at Vosen's willingness to kill CIA personnel, even ones who have sabotaged their mission, and could be considered traitors, like Nicky, and quits the operation.
But why wasn’t Landy outraged at Vosen’s willingness to kill Neal Daniels? What distinguishes Daniels from Parsons, when they’re both CIA employees and involved with Jason Bourne? Landy didn’t expostulate Vosen until Vosen ordered Nicky Parsons dead. Of note, the script differs from the movie dialogue. This script matches the movie’s dialogue.
You do not have the authority to kill her!
Oh, yes, I do. And you had better get on board.
Noah, she's one of us.
You start down this path, where does it end?
It ends when we've won.
When we're finished with Daniels, send the asset after them.
Yes, sir.
Although this final shooting script that DIFFERS from the movie’s dialogue, I quote it for more context.
LANDY You don’t have the authority to kill her or Bourne!
VOSEN Yes, I do Pam, it’s right here and it’s legal.
VOSEN slams a document on the desk. INSERT SHOT: “Blackbriar: Lethal Action Protocol.”
LANDY She’s one of our own. You start down this path...where does it end?!
VOSEN It ends when we’ve won.
LANDY turns and storms out...
VOSEN Notify the asset of the additional target.
BRYAN Yes, sir.
BRYAN codes in a kill order on NICKY...
In the final shooting script, Landy does confront Vosen in his office, regarding the use of lethal action against Daniels.
INT. VOSEN'S OFFICE
Landy enters without knocking.
LANDY
Since when do you have authorization for lethal action against Daniels?
VOSEN
Since he cleaned out a Blackbriar safe and fled to Morocco!
LANDY
So grab him-
VOSEN
I don't have the people on the ground to do that and I'm not going to risk that file falling into the wrong hands.
LANDY
What's going on? What's Daniels got?
VOSEN
What's he got? He ran all of Blackbriar's operations in Southern Europe and North Africa.
LANDY
I think the world's well aware we have a rendition and lethal action capability at this point, Noah.
VOSEN
For Christ's sake, Pam, he's got our entire playbook. Names, dates, ghost sites, how we train our assets.....
LANDY
You still don't have the authority to kill him.
VOSEN
Oh, yes I do, Pam.
Vosen holds up the file we saw him pull out of his safe. It is labeled "Blackbriar: Lethal Action Protocol."
VOSEN
That's what makes us special. No red tape. No more getting badguys in our sights and then watching them escape while we wait for some bureaucrat to issue the order.
Landy opens up the file. Sees the words "instantaneous lethal action is authorized when..."
LANDY
You just decide? No oversight. No checks and balances.
VOSEN
Come on, Pam, you've seen the raw intel. You know how real the threat is. We can't afford to have our hands tied like that anymore.
The Bourne Ultimatum (2007) - final shooting script
This scene was actually shot (with minor changes to the dialogue) but ended up as a deleted scene.
LANDY: Since when do we have authorisation for lethal action against Daniels?
VOSEN: Daniels cleaned out a Blackbriar safe and fled to Morocco.
LANDY: So why don't you just grab him?
VOSEN: I don't have the people on the ground to do that. And I cannot risk that file falling into the wrong hands.
LANDY: What's going on? What's Daniel's got.
VOSEN: What's he got? He ran all of Blackbriar's operations in Southern Europe and North Africa.
LANDY: I think the whole world knows we have rendtion and lethal action capability at this point, Noah.
VOSEN: For Christ's sake, Pam, he has our entire playbook. Names, dates, ghost-sites, how we train our assets...
LANDY: You still don't have the authority to kill him.
VOSEN: Yes I do. That's what makes us special. No red tape. No more getting the bad guys in our sights and then watching them escape while we wait for someone in Washington to issue the order.
LANDY: So you just decide? No oversight. No checks and balances.
VOSEN: You've seen the raw intel, Pam. You know how real the threat is. We can't afford to have our hands tied like that anymore.
LANDY: I guess not.
The Bourne Ultimatum (2007) - deleted scenes
Some of this dialogue was repurposed for a conversation between Landy and Vosen that appears in the movie around 42 minutes into the runtime. The scene occurs after the CIA's failed attempt to grab Daniels in Madrid, but before Landy is informed by Cronin that they intend to kill Daniels in Tangier.
LANDY: What's going on? What's Daniels got? What's Operation Blackbriar? Do you want to tell me, or should I call Kramer and ask him?
VOSEN: For Christ's sake, Pam, we're in the middle of an operation.
LANDY: Bullshit. You want Jason Bourne, level with me.
VOSEN: Operation Blackbriar started as an NEAT surveillance program.
LANDY: And what is it now?
VOSEN: It is now the umbrella program for all our black ops. Full envelope intrusion, rendition, experimental interrogation is all run out of this office. We are the sharp end of the stick now, Pam.
LANDY: Lethal action?
VOSEN: If we have to, sure. That's what makes us special. No more red tape. No more getting the bad guys caught in our sights, then watching them escape while we wait for someone in Washington to issue the order. Oh, come on. You've seen the raw intel, Pam. You know how real the danger is. We need these programs now.
LANDY: What's the connection to Daniels?
VOSEN: He ran all of our operations in Southern Europe and North Africa, so he has everything. Names, dates, ghost sites, who's cooperating with us abroad. Every operation. You want that stuff in Bourne's hands, out on the market to the highest bidder? I don't think so.
LANDY: Bourne's not after money. He's after Daniels for a reason.
VOSEN: Well, what does it matter what Bourne is after? When we find Daniels, and, believe me, we'll find him, if you're right, we get Bourne, too.
The Bourne Ultimatum (2007)
The fact that this dialogue was repurposed for a different scene which occurs before Landy knew about Vosen's intention to kill Daniels means that the deleted scene doesn't fit the narrative of the finished movie and is effectively non-canon. However, when Landy does learn (from Cronin, around the 47 minute mark) that an asset is being deployed to Tangier to assassinate Daniels, she tries to phone CIA Director, Ezra Kramer, presumably to raise an objection about it, but he refuses to take her call.
Her vocal objection to the asset being sent after Nicky as well is likely cumulative. It's safe to say that she already had misgivings about Daniels being on the hitlist, but she didn't have Kramer's support and was in a weak position to do anything about it. Then she finds out that Nicky is on the hitlist as well, and now that's two assassinations she objects to instead of one, plus the second target is someone she knows personally, which may or may not be a consideration as well.