It's a very interesting subject, but there are a lot of variables to consider.
When talking about perspective, such as size of subject with regard distance and framing etc. Plus, playback scenarios such as screen size and distance from screen etc. Then there is a good argument for saying that there is no subjective difference between the two.
But, when you take into account things such as actual resolved resolution of the sensor, then the subjective differences can change. Plus, probably the biggest impact on judging down converted 4K, but not the only consideration, is how the downscale is achieved with whatever downscaling technology is implemented. In fact, it's probably the downscale technology that is the single biggest deciding factor as to wether or not to use 4K for HD. This is why I would disagree with that particular video test, as there were differences that the tester didn't seem to pick up on.
Unless you are using a proper high end HD camera, there is a very good chance that you are not resolving full HD from its sensor. But if you shoot 4K and downscale to HD, even with a camera that is 4K but does not resolve 4K. There will still be way more than HD resolution to resolve from its sensor. And depending on the scaling method used, there will be full resolving of the HD resolution.
If you were shooting for HD and used a high end HD camera, then this would probably make more sense for the extended production workflow. There have been a few HD cameras that the film industry had no problems adopting, due to their outstanding picture quality and rosolving of resolution. Sony is probably most noted for this with maybe the Sony/Panavision Genesis being the most notable http://en.m.wikipedia.org/wiki/Genesis_(camera
Personally, if I were shooting for end to end HD and had the option to use a HD camera that could resolve the detail. I would choose that over a 4K camera. Even if the only real advantage was an easier pathway through the extended post workflow, through to delivery.
But none of this takes anything away from the fact that the subject is still very interesting, if not only for the fact that it is a source for a good argument