Sorry, SS, but I don't really see my reasoning as splitting hairs. And it fits within the logic presented by jkason as well.
If my character cuts a rope in order to drop an anvil on a foe's head, that's the same thing as swinging a sword to hit that foe, or throwing a rock. He's using a tool to directly harm someone, and he has to make an attack roll using his own abilities/BAB/whatever.
If he directs an already present sphere of flame to roll over a foe, that's the same as summoning a sphere of flame (a fireball) to fill the space inhabited by the foe. In both of those cases, the
originator of the action is
using a tool to
try to cause direct harm to someone else. The thing doing the harming is in the direct control of the person who wants to do that harm. To say otherwise would mean that casting Fireball doesn't break invisibility - after all, he's simply summoning a great heaping mass of flame that happens to be in the same space as that occupied by his enemies. That's not an attack, right? (
Now I'm splitting hairs . . .

)
If he cuts the ropes to drop a bridge - and all of the foes upon it - he's not using a tool to cause direct harm because in that case, it's not the tool that's causing the harm, it's the fall. If he summons a monster to attack, it's the monster that does the attacking. Yes, it's at his direction, but it's still the
monster that's attacking. He's not swinging anything, he's not trying to hit anyone on the head with an anvil, throwing a rock, trying to hit anyone with a rolling ball of flame. It's the monster trying to do the hitting. To say otherwise leads to the reasoning that if my PC makes an Iron Golem, and then the Iron Golem attacks someone who enters the room he set it to guard (with specific instructions that the Golem attack anyone who entered the room), the PC's invisibility is broken even if he's a hundred miles away.
In the case of a trap it's a little more blurry, but to my way of thinking the distinction is still clear. Although my PC triggers the trap, once it's triggered it's no longer under his control, and any attacks made use the traps stats, not my PCs.
So it looks to me like if an attack is made, and that attack directly uses the originating character's stats and abilities for resolution, it breaks invisibility.
OK, maybe it
is splitting hairs

. But at some point, somewhere, there has to be a line drawn. I haven't read the discussions on the Paizo boards, but it seems like on this issue there will always be debate about just where that line is and discussion is the only way to make that decision. The folks who are in favor of making invisibility more powerful do just as much hair splitting as those who want it limited.
And banning invisibility works for home games, but in a shared world that's not really an option.