I used to do a LOT of whitewater boating at a fairly high level. I paddled a C1, which is a decked canoe (looks like a kayak and is what they paddle in whitewater slalom in the Olympics--google Jon Lugbill).
A lot of raft guides carry knives, generally mounted on their life jackets upside down--the old Tekna knives were fairly popular. Gerber makes one. The general consensus among hardcore whitewater boaters was that this was more to impress the ladies than anything else.
No serious, high level whitewater boater I know carries a fixed blade knife, not a single one. The only ones who do are some of the guides who aren't serious hard boaters (kayaks and canoes) and novices. It's just not a good environment for a fixed blade. The guide in the OP is a case in point--somewhere, on the bottom of some river, are 8 or 9 knives waiting to stick somebody. Not to mention the potential for something happening when the things popped loose in the first place, even if they are not on a lanyard. There are cases of people getting hurt pretty badly when a fixed blade knife comes out of the sheath. American Whitewater compiles these things.
The boaters I know that carry knives carry something like I did--a Spyderco with a serrated blade. Mine secured very well in a small pocket on my life jacket. I never lost it in thousands of trips from Georgia to Pennsylvania and I never had to use it, nor have I known anyone who had to use one in an emergency situation to cut themselves or someone else free. And I paddled some dangerous rivers over a 15 year period. The only time I used it was when I broke a strap buckle on my squirt boat in the middle of Lost Paddle on the Upper Gauley. I used it to cut some old rigging off a buddy's boat to get another buckle.
Full disclosure: I still have the Tekna I carried on my vest for the first season until I wised up and started hanging around more experienced paddlers.
The fact is that tangling in lines is rare. Lines should be very well secured. If not the guide needs to learn more about rigging and less about knives.
I carried a knife because I like to have a knife and unlike a kayak in a C1 you are strapped in and though you can punch out easily enough it gave me peace of mind.
Most drownings out west are flush drownings (washing down a long rapid). Getting stuffed under a rock or tangled in a strainer (usually a tree) are the usual things in the east but happen out west too. I'm not sure I recall any drownings compiled in the yearly list caused by getting tangled in lines.
Should a raft guide have a knife? Sure, you never know when you might need a knife. But I feel strongly that the knife should be a one hand opening folder. Spyderco makes a blunt nose serrated knife that is perfect for the purpose. Figuring out a way to secure it should be easy. I had a short lanyard on mine and like I said it went in a pocket on the vest.
Sorry for the long post--this is a bit of a pet peeve with me.