These WRs are old runs, validated before video requirement for 1st place was a thing, so we let them there :)

Of course, it they're proven to be fake, they'll be deleted, but it's not the case at the moment.

How can they be proven to be fake without a video?

Idk, for example if extremely skilled players can't come close to the time even after hundreds of recorded attempts ? (20+ seconds gap for a 1 Cup run)

I was just throwing a thought there, it hasn't been discussed or anything, but it's pretty much common sense that if a run is proven fake, it can't stay on the leaderboards, let alone 1st place.