The cable prevents slippage in the direction of the current, just as a sailboat's keel prevents slippage to lee. What prevents the boat from overturning?? I suppose ballast, hull form and weight distribution just as a sailboat. The more surface area the keel has, the faster it would probably sail across the river. But like a sail, if it has too much area, the current causes an overturning moment which is too great to resist.
what keeps the boat from overturning? well, if i am to understand your description, you are talking about, basically, an upside down sailboat. one with no keel opposite of it's 'sail'.
to get to an answer to your question, you have to understand what causes heel on a sailboat. most people would say that the force of the wind in your sails causes heel but this is not entirely true. take a centerboard sailboat. sail across or up wind. the boat heels. raise the board. now, the boat moves down wind, instead of up or across, and heel will be reduced.
the keel, or other underwater foil, is responsible for heel. because the sails generate lift to lee above the water line and the keel generates lift to weather (in opposition to the sails, thus stopping leeway), there is a pinwheel movement generated around the waterline, which acts as the pivot point. this is heel. remove the lift created by the keel, which counters the lift created by the sails, and the boat simply goes the way the wind blows.
it's usually depicted as lever arms. one lever arm above the water and one below. the deeper the keel is the more heeling force it creates because it's like using a longer lever to lift something. sailboats are affected by a number of these 'arms'. ballast creates a righting arm that counters the heel created by the sal and keel.
fixed ballast on a keel acts differently that the moveable ballast of sailors on a dinghy. as the fixed keel boat heels, the righting arm of the ballast gets stronger as the heeling force of the wind gets weaker. in a dinghy, the righting arm gets weaker as the boat heels. it is strongest when the boat is flat or nearly flat. once the boat has heeled far enough the moveable ballast is directly over the center of the boat and has no righting force at all. a little farther over and it begins to get stronger; as force to help you capsize.
the boat you are talking about isn't acted on by forces on two different planes. it is only affected by one force. that force is the lift of the keel. the cable stops leeway. so, it won't overturn and needs no ballast.