The independent property of the CheckBoxTreeItem reads:

    /**
     * The independent state of this {@code CheckBoxTreeItem}.
     * The independent state is used to represent whether changes to a single
     * CheckBoxTreeItem should influence the state of its parent and children.
     *
     * <p>By default, the independent property is false, which means that when
     * a CheckBoxTreeItem has state changes to the selected or indeterminate
     * properties, the state of related CheckBoxTreeItems will possibly be changed.
     * If the independent property is set to true, the state of related CheckBoxTreeItems
     * will <b>never</b> change.
     *
     * @defaultVlaue {@code false}
     */

The docs don't clarify if an independent checkbox is affected by changes to its parent/children. It seems to me that an independent checkbox is fully independent in that it doesn't affect other items and isn't affected by them. I propose to clarify the docs to mention that and fix this behavior if it does not align with the docs in a followup issue.

https://mail.openjdk.org/pipermail/openjfx-dev/2023-January/037915.html