Frankly, we have no idea what information Karin gets from being a sensor. I'm inclined to delay spending too much time theorizing with the minimal information we currently have.
Fair enough.
If she's the agent of an SI and not one herself, they apparently sent her into a situation where she was likely to be in direct contact with a character who is infamous for his charisma (Naruto), which strikes me as pretty unwise if you want to keep an agent (as implied by the two assassins following her around). Adding in that she's an orphan and in some way aware that Naruto is related to her (meaning she has family) gives a good recipe for losing your agent.
Do note that,if she IS an agent, there is no guarantee that her handler is the same person that sent the two assassins along.
There is precedent for triple and quadruple-agency in Naruto.
But I'm coming to the conclusion that she worked for Grass Intelligence, and no one else.
She just provided corroborating evidence for the presence of at least two Players:
The Men in Black(Trenchcoats)
The Men in Capes
These people have been active enough(attacks in Leaf country?!) that the major villages will know of them, just like all the villages knew of and hired Akatsuki at one point or the other. Konoha even took MIB prisoners. So anyone working in Intel should know of them.
If Grass are aware of Karins strength as a sensor, it's entirely possible that they sent her along to the chuunin exams to gather intel, and she broke for it. And if they were using her as a long range scout as well as medic, it would explain some of how she has knowledge of multiple factions [headed by, staffed with?] transmigrants without actually knowing what their faction names are.
The presence of the assassins does imply that they wanted to secure her; whether safe from attack, or unavailable to the other side by any means necessary, we don't know. The fact that they only sent two implies they do not have full access to transmigrant intel, else they'd send better with a potentially A-S class chakra suppressor.
Yamanaka techniques can't read previous life memories according to her.
But that won't be any protection against present life memories, including any meetings or plots with transmigrants, which any Leaf mind-probe will find.
Including any convos with Hisana.
Given that she assaulted two members of Grass Black Ops, she isn't looking to go back.
So unless she has some sort of Mind Blank technique.....
*She was at the front of the formation, and noticed the sound team approaching from behind at the same time as Hisana, so unless is hiding her true abilities as a sensor...
We know what Karin's sensor range was at 16.
We don't actually know what it is at 13, even assuming she got training.