My assumption is that people have cheap high power ~50 mw rated green laser pointers of questionable origin. The green is generated by optical pumping with an IR laser. Unscrupulous manufacturers omit an IR filter, allowing the much more powerful IR beam to also pass. This is problematic because the laser eye protection you're supposed to buy to match the green wavelength wont protect your eyes from this. Anyway given the number of beams it seems like there could conceivably be enough power delivered to overheat or damage something.
I think most drones wouldn't be 'taken down' by lasers: flight control and GPS should still work fine. But seems reasonable that enough lasers could blind the camera, eliminating it as a surveillance asset.