I used to work for a company in the lightning prevention industry (yes, prevention). I've seen some amazing things lightning can do. Just because something isn't ypically a conductor doesn't mean lightning can't do some damage to it. Moisture will always play a part in the conductivity of things, like trees for example. It's the moisture in the tree that makes it a good conductor, not the wood.
That being said, mania is correct. Being inside of a car is a very safe place if you can get to one, but chances are, you can't (unless you just put in or are close to a take-out).
Definitely don't get out and park yourself under a tree to wait it out. I'd think you are better off in the river, even soaking wet, than under a tree. The other thing trees have is sharp points that create "streamers", which are little streams of electricity that join the "leaders" from the clouds to create a strike. Without sharp points, it's a lot less likely that a strike will occur.
I'd say your biggest danger on the river surrounded by taller ojects is the ground currents. If a tree near the bank were to get hit and the charge travelled through the water and you happened to be touching it, you could get a jolt. Depending on how close and how much water, it would disipate pretty quickly I would think.
If you are on a flat river (float trip kind of thing), you're probably more like a boat on a lake. In that case, I would think you might want to try to find a nice open area, void of any trees or other tall objects. Get to a nice low point (dried up ditch or something) and wait it out from there.
I guess it's a tricky question, because in some cases, there's probably not a whole lot you can do about it. It's really somewhat a game of chance at that point, so like Snowhere said, don't worry about it, at least not until you can do something about it.