Well, we have different experiences on this. I have raced and practiced at dozens of different mountains in New England and have viewed dozen races and training sessions that I have not participated in and out of all of those races both participant and observer, as I mentioned I only saw a course roped off once. Almost all race courses have a sign at the start of the course and often rope off the starting area. The video you cite is not from New England which is where I have had all my experiences. Pro and National and F.I.S. probably do things differently.
I am not doubting you. I never raced and you have much more experience in NE and in racing to base your statements on. I was just explaining why I would expect the course to be roped off. Because based on my experiences - they always are when run on a public and open trail. You are correct, this was the US ski team training, FIS I suppose, and they might have different standards and more resources available to them.
This is very educational for me though, possibly injury/life saving... based on my prior experience I could have ducked into a race course under the assumption of "not roped off = not in race use". Now I know not to do that.