"The infection was from drug-resistant staph bacteria. So John went back to the hospital and spent a month on powerful antibiotics pumped directly into a vein near his heart."

There are so many confounding factors here. Could be no connection to the episode whatever. Could be that the infection that required the antibiotics contributed to the autism. Could be the antibiotics contributed directly. Could be the overall trauma of the surgery, treatment and recovery.

Seems like the gut thing is the least likely culprit and requires quite a lot of creativity to even consider it.