Because a) it's not actually that much of a lie, and b) the alternative is nothing, which is much worse and liable to get us attacked, or them trying to take us in to discover where the intelligence leak.
1)Thats not how this works.
What you lied about is not as important as the fact that you did so in the first place. And once you are known to be a liar, people get much more cautious about believing you or negotiating with you.
We are currently roleplaying an Infernal Exalt and chief executive of a major nationstate. We are a social Exalt.
Being known to lie makes our diplomatic efforts actively worse; we still look and smell like an archdevil to the supernatural eye and nose.
2)No information is better than false information.
Your word once broken is very hard to repair. And these guys are a valued ally of the White Council; our telling them falsehoods is going to materially affect our efforts with the White Council when(not if, but when) it gets back to them.
3)They have access to people who can at a minimum talk to ghosts.
Ghosts and spirits know shit in this universe, and will talk to people who speak to them the right way.
We dont want to play ourself.
And here is where all your reasoning breaks down. You first need to explain how a known terrorist was able to operate like he did in order to ascertain whether us recognizing a senior member of the Fellowship indicates (to them) a strong danger to their operation.
My guess would be some manner of glamour / facechange magic. It's quite likely that they have access to magic. It's also quite likely that they can veil or change their appearance (hell, just regular plastic surgery would do that). It's also nearly guaranteed that they are often using aliases. We used the woman's real name based on her appearance. The woman is a leader of a local war party who was secure enough to operate in a public airport. She's likely here in disguise of some sort.
They do not have organizational access to face change or glamor in the series.
I dont think we ever saw a human magic user who was any good at face change or glamor in the series; that was an exclusively Fae or naagloshii thing.
Martin was very good at disguise, but he had no magical aids.
When the FBI were looking for him in Changes, he used a purely mundane disguise to stake out the FBI building.
My guess is very simple: fake passport(s). Same person, cosmetic changes to hair and appearance, from one of the laxer countries. Which is something money and connections can and will get you if you know where to look and grease the right fingers.
The PLO did it, Al Qaeda does it, the Mossad does it.
The US didnt start using iris recognition until 2014ish IRL.
And frankly, if I had to guess, its probably a lot easier to find someone who can work a ritual to sanitize your personal records in the US customs system, where you can pile successes from a ritual at leisure at an auspicious time.
Than to get someone to cast magic on the move.
No. She and hers confronted us with a threat of violence under mistaken assumption. You escalated to presenting yourself as a strategic threat to their whole operation, if not organization, with deep level of penetration into their security.
Respectfully? Thats nonsense.
Identifying one high profile agent is not a strategic threat to their whole organization; thats like saying identifying al-Zawahiri or al-Adel is a strategic threat to Al Qaeda.
Or that identifying one of El Chapo's senior enforcers is a strategic threat to the Sinaloa Cartel.
Wizards literally live on this sort of information access and control. So do the Fae.
This isnt exactly a new phenomenon to them; if that wasnt a manageable threat they wouldnt have lasted more than two hundred years and counting.
Now that she's figured Molly isnt a vampire, its a tossup between whether she's just fishing for information or unconsciously treating Molly like the teenager she appears to be.
Or maybe they got reports from 4-5 neighborhoods along the eleven hundred kilometer track and said "I think it's all along".
Maybe. I considered that.
But they mentioned picking up the trail where we left the river.
And we've only been in Mexico for around two hours now.
That suggests more coverage than just a couple outposts along the waterway, because you usually dont stumble into a person's tracks across eleven hundred km of waterway.
That or a passel of cooperative spirits or fae doing tracking for them, which is at least as significant, if not more so.