First off, thank you for your reply!
My diagram was conceptual and intended to focus on the direction of current only which is why I omitted the current limiting resistors. But perhaps to your point, I suppose it's better to be precise than not (notwithstanding that too often I'm accused of providing too much detail).
I've seen where people have driven multi digit 7 segment displays directly from shift registers or directly from controller output pins (and with proper current limiting resistors) which are set in code to be either high or low. It struck me that the OP was trying to do that (ie. limit to high/low values) and correctly pointed out reverse biasing concerns that result from that design.
What you really want is a high impedance state on the cathode rather than a high output to turn it off. That's exactly where I was going and as you correctly pointed out, that using transistors on the common anodes avoids this problem altogether (side note: I believe PNP is a good choice here). Furthermore, and of course, using transistors may also solve the problem of over driving the display directly from logic level outputs.
So unless I've either missed or misconstrued something, I believe we are in violent agreement!
P.S. I will add that if one can drive the display directly from logic level I/O, then changing the output to high impedance by dynamically changing it to an input can solve the reverse bias issue here. Having said that, Charlieplexing uses tri-state logic and yet still reverse biases the leds, so it may not necessarily be a big concern as long as you pay heed to the led data sheet's reverse biasing limits.