I can't see your example video due to restrictions on the network where I work.
What exact version of AE are you using (down to the last decimal)?
What do they look like in Premiere?
As I look at that clip, I see a poor recording in a highly-compressed video codec. If I were you, I'd talk to the guy who got them to work.
It is an unmodified clip without any conversion, it's what I got from my friend. It's avchd in an .mts container I believe. So the tearing is the fault of the recording and it is unrepairable? I will try to contact that guy, the problem is that I don't know him personally. Maybe he used clips which aren't tearing, and only some of the clips are corrupt like the one I uploaded, can that be the case?
Also, if needed, here is an unmodified, native copy of one of the problematic clips: 00134.MTS - Google Drive
The disturbance doesn't happen all the time, so the other editor may have simply cut around them. He may have found a few clips with no disturbance in them. All the more reason to talk to him.
If you have no other choice but to use the clips, you'll have to get resouceful.