I still think that they made it very clear on P.39 of the rules when they stated:
"In other words, if an opposing unit is destroyed during a skirmish’s resolution, each friendly card with the splash damage keyword is triggered."
When someone plays a Psionic Storm card from a supporting High Templar, its the front line unit that gets the kill that triggers the splash dammage, but the Psi storm's splash is not on the card of the FLU. The same with a science vessel and irradiate.
In both the cases were a High Templar or Science Vessel are all alone by themselves in a skirmish (So they are a front line unit in this case), they would not be able to trigger splash damage as they can't destroy a unit without another friendly unit with appropriate attack capabilities involved.
The Queen playing spawn broodling is not limited in this manner. Spawn broodling destroys a unit during the skirmish (assuming there is an enemy unit that meets the requirements of the spawn broodling card). So any cards with splash damage in that skirmish should be triggered.
That is just my take on the way it reads though.