Yeah I do not think that one video of carp in clear water proves that carp do not silt up a water body, the water there is deep and the bottom sandy..I've seen it too many times, take 3 clear dams, add just one or 2 carp into one of them and soon you will have 2 clear dams and one murky one. Occasionally they might not do it but that probably has more to do with the local environmental factors. Not silting up a perfect environment and silting up any other environment means that in general they create silting of the water, not the opposite. I've seen a few individual waters in my life that do not silt up ( Germiston lake, Sandvlei CPT, princess vlei etc) and contain carp but the majority do. A local very large dam has dried up somewhat, it has very healthy fish populations and lots of food. When one goes to the top where the dam is now in the old river channels and looks at the ox bow "ponds" that have been left, one can clearly see which ones trapped a few carp in them and which ones didn't trap a single carp. Some are gin clear and others look like roodeplaat, but they have the same water, same food resources, same gravel/silt/stone/clay bottom, right next to each other and like night and day one is pea green and brown muddy and some are clear all the way to the bottom. I cannot see one carp in the clear ones, just bass, barbel, kurper etc but in the muddy ones there are clearly carp jumping and rolling about.
That said the biggest threat these waters are not carp in the least, but as you said, pollution, water extraction, fertilizer run-off and silt from erosion are the biggest culprits.
Cool video that you found though, I find it interesting that the carp seemed to prefer the sweetcorn to the seed and boilies placed down..

Koo all the way..