As you can see in the video they add 1000 times the same feedurl. there is no reason to allow this so it would be extremely easy to fix for Netvibes.

Exactly, the onus is on Netvibes, not FeedBurner.

why should Net Vibes fix this? It doesn't affect their user experience one bit, why should they waste programmer hours fixing someone else's problem? For them its better to leave this thing open since it means more free exposure.

Net Vibes (and most other web-based feed readers) does not request the feed every time it is requested, they request the feed periodically if any of their members have subscribed to the feed. In that request they include the number of subscribers they are requesting for.

Net Vibes has implemented it slightly wrong and are sending the number of "boxes" that contain the feed, not the number of users who have at least one box with the feed.

So when Feedburner sees a GET on their feed with metadata from Net Vibes saying how many subscribers there are, they can either ignore it (since it can be gamed) or use it. I find it valuable that they use it so I hope that Net Vibes fixes it.

Feedburner could ignore huge jumps from Net Vibes but the attack would work with slower growth, leading to distorted statistics.

Because they're the ones that have the ability to fix it. FeedBurner can't determine the real subscriber number from the one NetVibes gives them, so it's up to NetVibes to report an accurate number.

Relying on a third party to "do the right thing" is a dangerous path to take. It's like putting up a robots.txt and saying it's up to the crawler programmers/users to respect the rules.