I'm no expert but I'm pretty sure thats not how a Brazilian wax is done. Yes, the waxing process is the exact same but the girl doesn't lie there full eagle while its being done. Its done in sections so that none of the "privates" are actually exposed entirely like it is in the video. Also, the video might be a little misleading along those lines, as the wax is obviously not being applied directly to the vagina. The sheet covers it but only a portion of the skin on the sides is actually being waxed. As such, thats why its possible to do the whole process without really exposing anything. That nudity in the clip is most likely for erotic purposes. (Who finds that erotic? No idea).
Aside from all that, as having been a victim of waxing, all I can say to you is: Ow.