It sounds fishy. It could be Guillain-Barré but I doubt a vaccine at 4 did that. It sounds like they contracted Meningitis and they didn’t get that from a vaccine.
Unfortunately there are many of these stories, like the baby referenced above whom many of us on FR are praying for. It pays to be cautious instead of embracing convenience of less visits with a larger immunologic challenge at each visit.
https://www.nvic.org/vaccines-and-diseases/Vaccinations—Know-the-risks-and-failures-.aspx
The CDC’s childhood vaccine schedule recommends all children receive 69 doses of 16 vaccines with 50 doses of 14 vaccines given between the day of birth and age 18. 36 The majority of children in the U.S. today receive three times as many vaccinations as children received in 1983.
The 2013 IOM Committee, which examined the safety of the current federally recommended early childhood vaccine schedule found that it had not been fully scientifically evaluated: