Thinking about that I think I figured it out. The earth is going 30 km/sec around the sun, so that's probably where the 30 km/sec comes from. 30 km/sec is well past single stage to orbit and they would not need a booster if they could get into that range.
Mars is doing 50km/sec around the sun, but you can cheat in a few places as your earth orbit can add ~8km /sec from orbiting around earth. That's 50 - 30 - 8 ~= 12km/s plus delta V get out of suns and earths gravity well. But you can also play with orbital mechanics to save some energy and you can also subtract the orbital velocity around mars.
Anyway, I am not sure how much delta V you need, but it's well under 30km/sec.
PS: Video had refueling in what looked like LEO, but if your in a higher orbit the craft needs less fuel to get to Mars from that orbit.
Maybe for course corrections where you need to fine tune the orbit a couple of mm/s here and there?
For unmanned missions it does make good sense as the mass doesn't grow so strongly if the trip time gets longer.