Personally i can't see the problem with using two rods, even on smaller rivers, thats if they are used sensibly.
I see so many times people using two rods both angled in the same direction, and sometimes the baits can't be more than a few feet apart, if we had a head scratching emocation i'd be using it now. Using two rods like this, then yes you are are asking for trouble.
When i use two rods, one always goes upstream, not just from a saftey point of view, but to allow two entirely seperate areas to be fished, dependant on the swim the baits can be as much as 30yds apart.
Using them like this most definatly has put more fish on the bank for me.
if a swim wont allow an upstream cast then it is only one rod out as i will not put 2 lines in one swim, as i'm certain in most cases it will hinder my chances of catching, at least on a small river.
But likewise if i cant get a cast downstream, i may if the upstream is an attractive enough proposition, use just one rod upstream.
As far as having two rods go off at once, it's never happened to me, but if i were fishing a prolific river, i'd consider whether it would be wise to use two.
I think a lot of the time some people use two rods close together sometimes on one bankstick with a bar because they think it looks good - scratching my head again !
My rods are kept either side of me, up to arms reach away if the swim will allow, and angled at about 45 degrees in opposite directions, this keeps the lines point of entry into the water as far apart as possible. The downstream line if the bottom is suitable is pinned down. The upstream flow will do that anway if you don't keep your line tight.
I've never had a problem fishing like this, nor even come close to having one, common sense is all thats needed to avoid problems, and realising that not every situation will allow two rods to be used safely.
Regards
Ian