That's on Worm's canon rules being they are, really. Wildbow declared that for a
Second Trigger to occur, it's not enough for things to be very traumatic. I can see the reasoning for this - given the kind of things parahumans get up to and all the traumas they endure, if trauma alone was enough then there would be a lot more second Triggers. But it happens so rarely that people are remembered for having Second Triggers than the opposite.
So Wildbow stated that trauma alone wasn't enough - thus bringing in the concept of Sechen ranges. For you to be closer to your passenger in terms of connection, you have to be in a mental state as close as possible to your original Trigger. For a Second Trigger? Basically you have to repeat the entire circumstances of what led to your Trigger happening, which is why not every traumatized cape gets bonus powers. Sure, you could lose all your limbs and suffer complete immobility for the rest of your life, that's traumatic - but if you got your powers from being beaten up and not from losing limbs then it doesn't matter for your passenger.
Here in Parian's case, it's basically that. She got really close to her Trigger circumstances - the feeling of being persecuted, the feeling of isolating herself due to her paranoia, and then destroying her reputation by blowing up in public and saying the wrong things, yes these are all things that Parian's Trigger was about. But without that last step, that sudden and immediate loss of a loved one and someone she cares for? Parian couldn't Second Trigger. Mind you, she was still very much messed up and having an emotional breakdown at the experience, yes, but ultimately her passenger doesn't care for what she feels so much as whether she was in the same state as to when her Trigger happened.
Nope, all of the explanation I just posted above? That's from LordRoustabout's WoGs shortly before, during, and after the charity show chapters. It had been repeatedly stated that the lack of the loss of a parent was what kept her from Second Triggering.
One such WoG.