Keep WooCommerce from mentioning backorders unless the item is actually out of stock

gistfile1.txt

add_filter( 'woocommerce_product_backorders_require_notification', 'jmg_backorders_notification', 10, 2 );
function jmg_backorders_notification( $notify, $product = null ) {
	if ( $product && 'notify' === $product->get_backorders() && $product->is_in_stock() ) {
		return false;
	}
	return $notify;
}

Here's what I saw when testing:
Allow backorders: “Do not allow”
with quantity 1: “1 in stock”
with quantity 0: “Out of stock”

Allow backorders: “Allow, but notify customer”
with quantity 1: “1 in stock (can be backordered)”
with quantity 0: “Available on backorder”

Allow backorders: “Allow”
with quantity 1: “1 in stock”
with quantity 0:

If a product is actually in stock, it'll only confuse the customer mentioning backorders (with Allow, but notify customer), but with 'Allow' if the product is out of stock and can be backordered there is nothing displayed at all.

This all came about because of this post in the WordPress.org forum https://wordpress.org/support/topic/available-on-backorder-2/