Motor Head Question

[Graueradler]

I was thinking about an experience that I had several years ago and remembered something that I had accepted but not understood (and still don't understand). I was trying to find the cause of a problem that after a no problem run-up would intermittently result in the engine suddenly quitting during the full throttle "take off" roll. Take off in quotations because once the problem occurred, there weren't anymore take offs until it was fixed. I found that yanking the mixture to lean would keep the engine running when this happened. The problem turned out to be loose parts from failure of the muffler internals intermittently partially blocking the muffler outlet. The explanation was that obstructing the exhaust makes the mixture go rich so that is why leaning would keep it running. The question is why does an exhaust obstruction make the mixture go rich (if it does). There is going to be less air flow through the carb because of exhaust back pressure but that should suck proportionally less fuel into the intake.