Of course they had luck (and more than a bit). But aborting safely would have required luck too. They were already off their pre-planned trajectory, which meant initiating an abort would have put them off of the pre-planned abort trajectory. So a successful abort would probably also have required manual control, and not just for the minute or so required to land, but for an extended period of time while they tried to figure out the right trajectory to get back up into lunar orbit and rendezvous with the command module.
Given that choice, I'm not surprised that Armstrong elected to attempt the landing.
Mission control would have had the trajectory back up calculated and in hand, but separating from the lower lander stage and engaging the (different) return rocket at low altitude, outside of normal flight parameters, with an ongoing computer problem of (then) unknown origin - I would agree, that sounds still dicier. Plus, a manual landing was practiced in computer-governed simulators; it wouldn't feel the same, but otherwise the task would be quite similar - except for the dust perhaps.
Given that choice, I'm not surprised that Armstrong elected to attempt the landing.