Just what are the rules? Is there a quote or WOJ?
Only what we can infer from the books but I think that is enough. Winter is about struggle for power. The dagger was just too big a temptation for most beings of winter. Trying to get stronger is what is expected from you in winter. It is all in what Lea teaches Harry as well.
Consider what Lea said in Proven Guilty when
Harry found her packed in ice.
That was about after she became infected. Before that, before the dagger, she was just the normal Lea. It was the struggle to preserve that Lea that drove her to Mab, because she was failing.
Then on the next page.
Perhaps she did grow arrogant with the power she held and that was how the Enemy was able to tempt her.
The dagger
is power, only magical power of considerable size can probably contain an infection.
She also thought she could over come the infection on her own... Knowing Mab as we
know her, unless there was mitigating circumstances like being infected, do you honestly think she'd even consider giving her a second chance?
Of course she was infected. What I read in your text is that she was infected before she accepted the dagger and that is contrary to what both Mab en Lea said and not a necessary condition for picking up the dagger in the first place because thirst for power is a perfectly acceptable motive for that.
She speaks of trust, if the Winter Court was all about power struggles as you suggest, it wouldn't be an issue...
The trust is in things typical fairy like not being able to lie and keeping balance. It is about the rules she can not break and oaths given. The infected can break these things and so can not be trusted.
It is about how Harry can trust Lea and can not trust Lea.
Especially before she got the Knife, if there wasn't evidence that she was infected before, I think Mab simply would have killed her, not treated her.
She was quite clear in dead beat about the value of Lea as a vassal. The point was that she could be cured and that it was worthwhile, the exact moment of infection was not really important for that. The other thing was that she was her vassal and asked her liege for help. Mab might not even be able to refuse that help under these circumstances.