So. False Report.

Without absolute confidence that the opponent has nothing splashed into their deck, and barring a case where you're sure you can end the game that turn, is it ever safe for the DS to destroy a LS objective?

Because False Report will, more often than not, end the game when it appears. If both players have any sort of board developed, it wipes both and gives the LS a free chance to deploy and go rampaging. Unless you're in a very strong position on your objectives and their damage, it doesn't take much to end the game right there.

Barring holding a comparable wipe card (Force Storm, maybe) is there anything at all you can do? Or do you just scoop your cards when False Report hits?

Play enough probe droids and get enough damage on objectives that you threaten to win if they trigger False Report.

Never done it myself but I've heard it's awesome

Not every deck uses False Report. Even then once dial is a 6 an aggressive Navy deck will just win. Doesn't matter if False Report was there or not.

False report isn't too scary.

I've found that if my opponent hasn't played a free-holder turn one against an aggro deck I may as well blow up as much as possible. All their units return to hand as well, so unless they have oodles or resources or were hiding free-holders in hand they are probably too close to their reserve to draw any new ones. Now DS turn 3-4 it can be a problem but if you save up enough blast you can win with the dial at 6 (or 5 with devastator).

Like Mac mentioned I've also blown up 2 to put the dial within three and damaged the third one enough that my probe droids would kill it, forcing them to not trigger false report, it's good fun.

Yes, if the deck is tooled properly, it shouldn't be an issue.

Also, The False report is S&S affilation only, so anybody who doesn't play S&S is safe to squash.