To me it looks like the first guy on the raft does have a flip line around his waist (0:59) and is working on a locking carabiner. Don't know why he didn't use it, or maybe it wasn't a flip line. I'm a proponent of righting a boat ASAP, in the current when possible, but obviously there are exceptions: high consequence hazards just down stream, boats too big/heavy for 1 or 2 people to right, etc. It's hard to know in this video if there were some extreme hazards we can't see, or don't know about. I do think they had several opportunities to right the boat sooner, but what does this armchair QB know?
I don't wear a flip line, generally. If I do, it's a 6' NRS strap with a couple of daisy loops in it to keep the tail reasonable. I no longer wear the 10' long, 3 times around the waist webbing kind for a variety of reasons:
1. I've been clipped into things I didn't want to be clipped into. More than once- not a fluke.
2. Knots are uncomfortable.
3. I am typically faster using my paddle to right an upside down boat, since I don't let go of it when I swim, and don't really want to let go of it to fart around with a strap/line.
4. I can often right the boat without getting on top of it: fingers in the drain holes, elbows on the tube, and do a curl.
5. I rarely need one in the first place.
6. I keep flip lines (NRS straps) in my PFD, which are a total of maybe 3 seconds slower than one on my waist.