There may be something to this.

However, we also should think from a design perspective. Let's say you're the guy who has to come up with the art for a new logo. It needs to be simple and recognizable. It needs to be something you could ideally draw easily by hand, something you can put on a billboard and have it be seen and easily recognized from a great distance. So, you use a maximum of 2-3 colors. You use big bold forms. You can't put 13 stripes or 50 stars on a logo like this. Too complex, so you simplify.

3 is a very powerful number. It seems to resonate with people. There's a reason all the great Roman orators spoke in 3's. Think Julius Caesar's famous Veni, Vedi, Vici, for an example. And it works visually as well.

As for red, our nation uses red, white, and blue. GOP uses red. Dems use blue. If you need a third color (white and your team's color), you add the other team's color and use the American trifecta palette. It's pretty standard for political messaging. Again, you don't use more colors than that because you start thinking of printing costs for signage and letterhead and all that. More colors = higher cost, so you pick 2-3 max.

So, while there may indeed be a Chinese connection, I'd prefer to see some better proof connecting the two. For now, I'm going to regard it as coincidental, and assume that they were simply following pretty standard design principles.