My iphone says apple will change battery free of charge, apple wants to do software update

My iphone 11 is giving battery calibration error as long as I remember. I didn’t care much and , I ‘ve been using it like this for few years. Its original battery and I m the first owner. Finally battery health dropped to%79 and i visited apple store. Msg says “ recalibration was not successful an apple authorized dealer will change free of charge “.

Guys in the store told they charge $100, when I show phone, they said they never saw this message before. They told me they can change but they wanna try software update first. My question is, How Im gonna know they wont cover up faulty battery with software patch?b