Oy! Indeed, that's a convoluted set of stream directions. And over a small stretch of territory, not terribly rare. Figure if the land is flat enough, another two or six or ten feet of depth would cause an outright lake, from leftmost bank to rightmost bank. Then imagine the water dropping a bit and the very slightly higher land happening to be in the middle of the whole area splitting the watercourse into two, or ten. Which way the actual movement of the water occurs may be as much a matter of current striking the basin >here< and sloshing >thattaway< and etc. -- like currents within a clear, wide lake can flow this way and that according to entry of streams, bottom topography, winds, and the like.
Note though that the streams in your example do rejoin - as such, it's more a case of 'stream threading' than 'stream divergence'. Such islands or systems of islands can stretch a long way. If it's happening near the entry point of a larger body of water, it's a delta, and technically is divergent. What you *don't* see is a river forking mid-way across a county or nation, choosing to flow into widely disparate oceans or lake basins. Note the scale - how long are these several islands you show? Usually they're no more than a hundred yards or a mile or three long. Fair enough: there's such an island maybe sixty miles long in Argentina (between Rosario and Buenos Aires) - still, think of it as a bit of river that swells to some fifteen miles wide, happening to have an island 14.5 miles wide in midstream.
The absolutely delicious extreme example is the river that flows out of Cambodia... except when the river it flows INTO rises by just a foot or two in flood season, whereupon said tributary actually reverses flow and actually runs back INTO Cambodia. All so very flat that a difference of a foot here or there drastically shifts the local stream pattern. Look at the Suudd in central Sudan - nastiest swamp in Africa; stopped upstream exploration on the Nile for half of *forever*. It shifts and twists and channels open and close and generally act unreliable and sneaky. I bet that a honkin' big rainfall like a prolonged nor'easter coming ashore will temporarily alter the pattern you show in the example --- a serious flood like happens on the Mississippi, Missouri, etc making *permanent* shifts (for values of "permanent").
So yeah - that example bends the rules; such rules being more rules-of-thumb than laws. What one ought to avoid in fantasy topography construction is egregious flaunting of the river-layout-plausibility-suggestions :-) by making rivers that divide and rejoin across great swaths of non-flat territory, and ones that run 'downhill' in more than one direction. Indeed, done right, showing threading and meandering and suchlike big complex-flow island-networks can be a huge indicator that the terrain is flat-flat-flat, and borders on being swamp/bog/marsh/bayou.
Mark's guess than man's interference could be at play is another possibility. As meanders shift a riverside port away from the main channel, locals may dredge and dike and meddle to get the nice profitable barges and paddlewheelers back in town. Canals need not be ruler-straight; indeed long ones follow terrain (sidehill instead of downhill, if they're trying to avoid locks) and can work up into the kind of network of his Rhine-Main-Danube area, or the tangle the Rhine & Meuse make when they hit the Netherlands.
Almost any rule of laying out topography and hydrography can be 'broken' , just at a cost of explanations needed to keep plausibility. A tenet of storytelling is that one does not include details that detract from the story itself - but if odd, unique, strange details actually contribute to the story your map tells, then go for it !
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