This is totally correct. Just to add how they do it, it’s in-line filtering. The juice goes through a pipe at high pressure though a filter and all the solids are removed through this process. This is used for many edible liquids. Almost all beer is filtered in this way for example. Most varieties of beer are cloudy without filtering. The filtering of juice (and beer) increases the shelf life. In addition it makes the juice easier to turn into juice concentrate. In my country at least all the big juice brand are just reconstituted juice concentrate. Juice concentrates are by far cheaper in many regions because they are traded as a commodity on the world market so you can source it from the cheapest source. Fresh juice however has to be made locally and has a low shelf life, hence the higher price.