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The change jerseys rule is not really for mixups in the book. It is to deal with deception...a player changing numbers to start fresh on their foul count or to confuse the opposing team. They do that, they get a T. There are exceptions for blood or torn jerseys but those sorts of changes must go through the scorer and the official so that every one is aware of what is going on. This is not for when the names and numbers in the book are mixed up. It is for when the book is correct to start and they change to a new number.
When the names and numbers in the book don't match the player who has participated, that is an administrative error. The names and numbers in the book both matter. The name is the base information and the number is just an identifier used to log activity. If John Doe is wearing 42 and the book has them as 24 while Jimmy Doe is wearing 24 and the book has them as 42, that is an error in the book and must be fixed at the cost of an administrative T. Switching jerseys to match the book is not allowable without penalty.
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