I know they got pulled into it because the client's father was a homeless vet who was one of the victims of the secret society/pych experimenters. (In fact, the episode opened with them throwing a body off a bridge, I think. Getting rid of a body, at any rate.) She (the young, attractive client) told them that the cops didn't care about homeless people, and weren't they supposed to help the helpless?
And somehow after that Hardison ended up mostly naked (yay!) and Eliot ended up at the shelter where they found out that the homeless vets were being culled for the "psych" experiments.
The blonde cop had initally met with Sophie and Eliot, and made her frustration with the whole situation clear - she knew bad things were happening and the whole thing was dirty, but wasn't able to do anything about it. Then she walked out of the room and left the file on the table so they could read it. So she was a sympathetic local who was willing to go over and aboveboard to help them out.
But I have no idea, really, why the secret society and psych students and CIA all tied together. I'm sure I'm missing lots of details, but mostly I'll just enjoy Hardison and Eliot taking on the interrogator in all their scenes together.