It does not seem fishy to me, because it is possible for pseudomonas aeruginosa to end up in a bladder after accidental catheter contamination.
If the urethral opening is not disinfected prior to insertion of the catheter, then bacteria on the perineum can be transferred into the bladder.
Once in the bladder, the bacteria starts reproducing and can take anywhere from a few days to a couple of weeks develop into a symptomatic UTI.
The doc's connection of the infant's pseudomonas UTI, to the catheterization, makes sense when you consider it from an epidemological perspective. The pseudomonas is the agent, the infant's bladder is the host and the catheter is the vehicle of transmission, once transmitted the bacteria thrives in it's new host until it is treated with antibiotics. Hope this makes sense and hope that the infant is feeling better.