Apologies for the late response. Please don't consider this a proffesional opinion, rather a semi-educated one

I presume a lot of this would be consistent with lightning safety procedures in the mountains as well?
The short answer is: you're only safe from a lightning strike if you're in an electrically shielded environment (i.e. enclosed in a conductive cage, which ideally should be earthed too). This is why you are relatively safe in a car (not because the tires are rubber). When considering the risk of getting struck by lightning in a particular area, the ground flash density (average number of flashes, or strikes, that hit the ground per sq. km per year) for that particular area needs to be considered too. Protection measures are normally implemented at sites as a function of both ground flash density and also the type of site (eg. an explosives factory would require much higher protection than an office building).
In general, the safety zone for lightning is a radius of 10km (note that if you're using the Flash-to-bang method of calculating the distance that this relates to almost 30 seconds). Higher elevations and tall free-standing objects (like large trees) should also be avoided (so being on the water a few metres from the nearest tree branch is safer than being on the bank under a tall tree). This is because if the tree is struck by lightning, the flash will travel down the tree and could possibly see a human body as a better path to earth (wood is not a very good conductor) as it gets near the ground and arc to it. This is known as a side flash, and can also occur in open, unprotected (i.e. not properly earthed) shelters (eg. picnic shelter). When lighting strikes the ground, it also causes a Another thing trees is that they tend to explode when hit by lightning - the lightning current causes the the small channels of water in the wood to flash-boil. If you're stuck in open ground (i.e your head is now a relatively tall, free standing object) the only thing you can do is to try and find the lowest point, and crouch down as flat as possible, keeping your feet together.
So, back to the river. Obviously You're also much safer being on a river (as opposed to on top of a mountain) because you're already at the lowest part of a valley (dependant on the steepness as well I think). I guess you could follow the logic to say that you should find the lowest point nearby, like just in front of the foam file, and stay there until the storm passes

Seriously though, if it's a park and play spot, the best thing to do is climb into the car (as long as it has a metal roof and the windows are closed) and either wait it out or go home. Somewhere like Gatsien, the best thing would also be to leave before the storm gets there. Although when I did get stuck there a while back, we ended up waiting out the storm in a bit of a depression on the left bank under a raft, well away from the trees. Does anyone know where Steve was when he was struck?
The bridge at Sierre is probably a better target for a direct strike (depending on how high above the water it is) but it could potentially flash to the water depending on how the bridge is earthed at either end, soil resistivity, etc. It's also possible to get injured during a lighting stike from an upward leader, which the bridge would not neccesarily protect you from. A lighting strike happens when a downward leader (from the clouds) meets an upward leader from the ground (the main current of the strike actually then returns back up this channel to the clouds). Many upward leaders are formed from all nearby prominent object though (as the downward leader gets closer to the ground), and these can have currents large enough to cause injury should you have one go through your body. So you don't actually have to get struck by lightning to be injured by it. (This happened at a local soccer game a few years back).
Ok, sorry, this turned into a bit of a collection of lightning trivia, and a bit longer than I intended

Hopefully it's vaguely understandable though, bit of a complex subject to explain in a forum post though...