Lets see now---I have a quilted table runner with batting that my DH spilled coffee on. I have a flannel back , no batting table cloth that my DD spilled red wine on. The coffee stain I can still see, the wine stain is barely visible. They have both been washed a few times. I think the batting holds the stain even though the fabric releases it. I'm getting ready to quilt a Grandma's Flower Garden, using flannel for the batting.
(On the lighter side, after the pandemoniam settles down and the covering is in the washer, and the apologies and guilt complex are the major topic--think! This is your moment, like "Would you like to help me paint the bathroom this weekend???????/")