Which got me thinking... Who are the PCs in this picture? The three at the bottom? If so, what if you're playing Batman?
A few weeks ago, our Star Trek crew found all their weapons and shields mysteriously failing, in violation of the known laws of Treknobabble physics. Contacting Starfleet we discovered the problem was fleet-wide, and we had to fight a boarding action while our defences were down. Finally power returned, and we learned that another Starfleet ship had been arguing with a Godlike Being that humanity wasn't a race of savages and that our weapons were for self-defence. The GM explained that this kind of thing must happen all the time in Starfleet.
I was amused, but I wouldn't want it to be a regular thing. (This was one session out of a two-year run.)
When you're really crossing over with something else - like The Watch House was in the same time as Buffy - then having events from the other stories affect yours is a good call.
When you're not - this wasn't a particular episode of Trek happening offscreen - then it's just the GM simulating a wider world of stories, and the players could reasonably expect a role in resolving things that affect them. After all, we have plenty of uncontrollable external factors in games already, and in life, and this is one area where the guy responsible for "acts of God" is across the table.
Throwing in complications the PCs can't really affect is fair enough, not much different than weather or other such conditions. Having the world end because a bunch of NPC heroes failed to save it would be a bit much...