"Brooks mentions that were legends, but Shepard doesn't mention the other crew-members and the ME2 squad-mates as legends, which they are, for helping defeat the collectors."
I don´t think it´s part of the general public´s knowledge the cerberu´s normandy incursion to collector´s space. According to both Kirrahe and padoks, the missions to construct the crucible and the omega 4 relay trip are top-secret. If you bring Padok aboard and mention about mordin having died, he will say that the salarian goverment ant stg are aware of the omega 4 mission. I don´t think he would mention stg if it was common knowledge. It must be top-secret, something only know to few top-ranking leaders, intelligence people or information brokers.
It´s possible that brooks, posing as an alliance bureaucrat was not supposed to know, she only tried to sell the notion that she knew the normandy from the citadel mission (me1), the efforts in the war, and maybe (if applicable) shepard´s mission in batarian space. The fact that she knew about the suicide mission war part of her big reveal.
Liara is naturally curious. She always investigates Shep´s background in me1, so it´s very possible -now more than ever since she´s the shadow broker - that she would read about kaidan´s past. i would not be surprised if she had more info on jenkins than the player. Remember, she is a big fan of the SR-1 and what that ship represents.
Also, she was still living in the normandy during the collector ship attack. Even if she was just recruited prior to Illos, she still resided on the ship for several weeks. It´s more than enough time to hear about Jenkis and the virmire victim from the survivor, or Tali, or the doctor... So it´s perfectly possible that she has insights into kaidan´s personality just by hearing about him or reading about his service record. She deduced a lot about the prior shadow broker´s background.