Simpler would be for the rental companies to put a sign prominently in the rental vehicles indicating the height of the unloaded vehicle, so the driver is aware of this being a large vehicle with restrictions on routes. Then again, most time the renters probably did not take the full insurance option, as it is a big part of a single day rental price, and often is not shown in the advertising for the prices, and thus they are liable for all accident costs.
From discussion on the comments on the page there is a strong likelihood the rental companies come out ahead, older vehicles hitting the bridge get written off, and the driver has to pay for a replacement vehicle as compensation, unless they took the insurance, which the rental company then use as payment on a new, higher value, rental unit. Newer vehicles will be repaired though, still coming out with a new body on it. As most are generally out of state that hit, or day rentals going through, the locals obviously are well aware of the limitations of the bridge, even though there is a municipal bus route that goes under it the bus is definitely low enough to clear it.
By me there is a double deck tour bus that runs regular, the metro has trimmed the trees to allow clearance, though when they ran the route the other way they did do quit a lot of large branch removal.