Plenty of quacks follow the principle of "do as I say, not as I do." It's a very common behaviour amongst populist politicians to talk shit about vaccines and then being fully vaccinated.
I didn’t read the article, but isn’t it plausible that whatever they did allegedly did wrong wasn’t significant enough to warrant recommending against taking the vaccine?
They didn't recommend anything against the vaccine. It is just overzealous fact-checkers who (similarly to antivax) couldn't admit that they were confused about the article and mislabelled it as false.
