Running Benchmark AHB2 in bridged mode and 4 Ohm Speaker

The Stereophile graph referenced above is done at 2.83V which is equivalent to 1W/8ohms and 2W/4ohms. 
Obviously, whether bridged or in stereo mode it won't be effected by any insinuated current limitation.
What will effect the simulated speaker load is higher output impedance - which is doubled with the bridged amp - but because its already usefully low this won't make a substantial (read audible) difference.
It certainly won't turn the bridged AHB2 into a tone control - which is a ridiculous exaggeration - especially in comparison to any tube amp or many other SS amps for that matter. 

An amp that can put 480 watts into 4 ohms can put 240 watts into 8 ohms so it can double from 240 to 480.  You can just think of it as an amp that puts 240 watts into 8 ohms and doubles into 4.  Its ability to put more than 240 watts into 8 ohms isn't that relevant.  Regardless of how you think about it, the amp delivers more current in bridged more.  At any given volume the bridged amp will have better current capability.  At 100 watts into 8 ohms it can double to 200 into 4 and again to 400 into 2 ohms since we know it can deliver at least 480 watts total.  A speaker is a passive component so obviously increasing the power delivered to it increases the current.  How else could it be?  

The issue here is not the amplifier. It is the speakers. If you want high quality and high fidelity then 4 ohm nominal speakers are definitely best avoided. The very low impedance is bound to create amplifier issues (stress) with almost any amp.

At any given volume the bridged amp will have better current capability.

Current capability will be the same (29A for AHB2).  Bridging just doubles output voltage.