Hmm, interesting!! Are you talking about non-optically pumped diode lasers in which an external current induces lasing?
But then you are now no more really talking about a closed system. The above statement is strictly true for a radiative closed system. If you bring in particles from outside you are no more talking about two-level systems.
Now if you use inelastic collisions to pump the electrons to upper levels, my guess is the inelastic collisions will work both ways i.e., even excited state particles can collide with the low energy particles which have just lost their energy by collisions and the two rates may equilibrate. Why should reverse process be restricted i.e., process A to B should be same as rate of process B to A. But you are correct that if such a collision process exists, then surely you would have a laser.
For example A to B process could be a chemical reaction in which A to B is an excitation process and the equilibriation rates can be such that B > A.
I wonder if you have looked at chemical lasers? I do not have much idea about those. It maybe possible that they do break the two level rule you talk about.