Its not about the water, but the land at the side of the water. You are quite right to say that the water is the pathway however, in legal terms trespass applies to land not water The civil tort is quite specific in this area. Unless you are a north Korea Gun boat.
Just out of curiosity I do a bit of canoeing and would I be allowed to fish whereever I like as I am not on any bank??? Also how would you fare if you were actually wading in the river and not on any banks or would this class as being on someones land as you are on ground?? Always wandered this so no harm in asking the more knowledgable 
Think of it like walking along a public right of way through an Orchard. You can walk through but you can't' touch the apples as they don't belong to ya' Canoe along a river but don't flip with the fishing rights.
But if the fishing rights are from the bank and you are in the water then the controlling club dont own the fish just the bank rights so it would be ok ????? Your response did'nt answer the question mate.
quote "Also how would you fare if you were actually wading in the river and not on any banks"
The owner of the land to the right of the river owns the river bed as far as the centre of the river the owner of the left bank likewise owns the bed to the centre on his/her side. The Water however is owned by neither and is the property of the relevant river authority.
The EA or Water Company own the water but not the land that the water flows over (in most cases) The rights to the land will be contained in deeds and the land owners investment in fish stocks is similar to the rights of farmers to graze beef or sheep on common land.(with public rights of way) You can't take the beast as it does not belong to you. When the river is low, the land owner has greater visible assets. Legally many boundries are adopted at the centre of a river for land rights.
So technically you can fish untroubled from a watercraft and the bodies to enforce any fishing rights are the authoroties that control the water E/A, B/W etc and the bankside owners would be powerless to stop you?? As I said I'm just curious as I only use my canoe on the severn and mostly on lakes and the sea I aint seeking any information to go pi55ing fellow anglers off by ploughing through their waters and setting up shop 20 yards downstream and fishing for free [B)]
I used to fish a stretch of the river Dane near Davenham that Davenham AC had "rights" to but during a match one day, a couple of gents set up pegs on the oposite bank to where I had drawn and basically told me to f* off as the land belonged to a farmer who said they could fish on his land for free. Cost me a fiver!! Very frustrating as the river was onlt 7 metres wide. Sh*t happens.......