It is absolutely a risk in a pool, but quite uncommon. In my experience the culprit is usually a spa pool, but swimmers are moving from the spa to the pool and carrying the organism with them. I would carefully check her history, I'll almost bet that she was in a spa and didn't tell anyone. It is also going to be fairly hard to inhale the organism from a pool, as the water is not aerosolized like in a spa with the blower or jet pump on.
In both scenarios, the indication is that there are times when the chlorine levels dropped. In the spa, the Pseudomonas can attach to surfaces if the chlorine is low enough, long enough. Once it attaches, it develops a "slime" layer or protective covering. The "slime can harbor a whole community of different kinds of organisms. This surface attached colony is not common in the pool due to the water temperature and more consistent disinfectant levels.
Maintaining a consistent level of chlorine is the best preventative. Once the organism colonizes, I would suggest calling your local health department for disinfection directions. Interestingly, Pseudomonas is often found inside the piping in both pools and spas. For some reason, the organisms in the piping seldom seem to cause problems. Usually if a spa is contaminated, you will find a slimy coating on the spa skimmer walls just at or a little above the waterline. This is not the grease buildup, but in large quantities looks like a clear, brownish jelly.
Incidently she didn't have "strep throat" if Pseudomonas was diagnosed. This organism usually causes atypical pneumonia when it get in the lungs. It can be serious, if not diagnosed in time. If the Dr. diagnosed strep throat caused by Pseudomonas, then someone is not being honest, or not informed properly. Be careful about admitting any responsibility, the source could easily be someplace else other than your pool, and it would be almost impossible to find after the fact.