Yes, then their only option is to ask nicely.
The corp will tell them to go to hell, and that'll be the end of that.
Or
The Corp will check with their "special procurement" division and find out if this person or persons are known, and what their value rating is. If said individuals are not known, or are known but have a bad value rating, they might decide to hand over info, or not. Depending on said Corps relationship with Lone Star.
Remember Extra Territoriality ends at the gate. If Toys'n'Stuff wants to be able to chase a runner team that stole their prototype assassination toy, they need good relations with LoneStar. Tell Lone Star to go jump in a lake, and their reaction times might get disturbingly slow. Do it often enough, and they might start harrassing your security teams when they're on Lone Star controlled turf.
I would be very tempted to roll an 'edge' test for the team, when they do a run.
Take the average edge score for the team, and roll that.
Every Hit buys off a point of possible trouble.
A Glitch means that something goes well for the 'detectives'
A crit Glitch and Ye-awww
Give bonus dice based on how thorough and detailed their plans were.
Allow players to chose to spend edge on the roll, to bolster it.
Maybe do a basic "investigation roll" to see how effective any investigation is. The dicepool being modified by who was hit, and the resources available. How big was the body count. Where was the body count, how politically damaging was the run, etc.