From what I read in that release, it wasn't a possible tire manufacture problem, but a possible mounting problem. I can imagine, for example, that one of the machines used to mount tires at the factory (or subcontractor) was out of adjustment, or had some damaged part. This might have cut the sidewall or bead of some of the tires.
Once Toyota became aware of such a problem (whether from customer complaints, or during equipment maintenance), they would have traced the problem both back to the offending machine(s), and forward to cars that might have been produced during the offending period and assembly line. The trick is to catch all the potential problems, while minimizing damage to Toyota's reputation, and inconvenice to customers and dealers.
paulj