The last drop might not be a superpower battle gone wrong in the vicinity of a kindergarden (the MCU has not established many B or C level superheroes and villains to copy the exact events from the comics) but something similar might happen which prompts Stark to join with the government against Cap and voila.. Civil War.
Based on the just released synopsis, it sounds like the MCU version of the registration act is going to be focused specifically on the Avengers themselves, rather than superheroes in general, which I suppose is a pretty good way to circumvent the commonly cited problem of not yet having enough characters to really portray the story properly.