Co-author here. We designed a statistical model, which is never 100% sure a re-identification is correct. There is, e.g., a non-null probability that two individuals in the US share 5, 10, or even 15 demographics attribute.

Good question. I'd also assume that re-identification chances would always be of the form 100/k (k being the integer number of people who fit the bill)

Perhaps the risk that some of the data the probability is based on is wrong, e.g., "She fits the bill except they only have 4 children and the 5th is an entry error, so it's not her."