Yeah, that's one reason why the arithmetic is crude. The PDF says the following things:
About 1/3 of US adults have been arrested by age 23.
About 1/3 of US adults have a criminal record.
Black men in the US are about 6x more likely to be incarcerated than white men in the US.
These figures aren't all about the same thing -- different classes of (alleged) offence, and also "adults" versus "men" -- and indeed the black:white ratios may be different for arrests, and criminal records, and incarcerations.
It's not obvious to me whether we should expect the black:white ratio to be much higher for incarcerations than for arrests or criminal records. If it is, then that would indeed be one of several possible explanations for how the crude calculation ends up with more than 100% of black men in the US having a criminal record.
Anyway, my calculation just pretended that the black:white ratio is the same for arrests / criminal records (take your pick, both are alleged to be up to ~1/3 of US adults) among adults as for incarcerations among men. Probably false, but I was just looking for a ballpark figure.