I had a mild case of PF a few years ago. For several weeks I could only run courses that were straight out and straight back. Left and right turns were painful. I had a 5k coming up that I was running with my niece and wasn't missing it so rest wasn't an option. I know how painful the mild case was. If JBo's was worse even at his age I can't begin to understand how he was playing basketball on it.
I still like to run several 5 and 10 k's a year. One of my favorites used to be the River Run in April in Iowa City. Any runners out there who would like to share their stories/injuries?
I used to run in college and there were several people on my team who got plantar fasciitis. I ended up getting it after college and some mornings felt like I couldn't put any weight on it. So I went to the doctor and he told me I should give up running and pick a different sport. HA HA fat chance. After consulting other medical professionals and some of my old teammates, I took some time off, switched shoes, came up with a preventative regimen, and now after some time off, have zero problems with it.
The solution for dealing with it in season when preparing for big meets or hard workouts was always to warm it up and rub it out with a golf ball. I can't personally speak to the efficacy of those techniques, but they were able to compete at about 80-90% when pushing through the pain. For a skill sport like basketball, I'd imagine that it's quite tough to deal with, but not impossible. I could definitely see it throwing off your shot or preventing you from pushing off in the way that you'd like to.