[1] e.g. https://news.ycombinator.com/item?id=32925763 among several others.
So I'd say it's more than "parent complaints". The books under discussion are not accessible anymore according to PEN's definition.
> PEN America defines a school book ban as any action taken against a book based on its content and as a result of parent or community challenges, administrative decisions, or in response to direct or threatened action by lawmakers or other governmental officials, that leads to a previously accessible book being either completely removed from availability to students, or where access to a book is restricted or diminished.
Parents saying "I don't want my kids reading this" is very different than a parents' complaint which reduces access to or availability of that book.
"PEN America defines a school book ban as any action taken against a book based on its content and as a result of parent or community challenges, administrative decisions, or in response to direct or threatened action by lawmakers or other governmental officials, that leads to a previously accessible book being either completely removed from availability to students, or where access to a book is restricted or diminished."
It sounds like PEN would not consider just a complaint they heard a parent make about a book as a ban on a book. If an entity that has books restricted or diminished access to the book because a parent (or other group) complained, PEN would consider that a book ban.
That is a rigorous and unbiased definition of a book ban.