If it was a premium cabin ticket it should have been allowed. However, I know that status related perks only apply to the status holder and guests when traveling together with the number of guests receiving benefits capped based on level. So if you were not traveling, your family member would not entitled to your benefits. Years ago (you can probably search the threads) the booking person’s status used to apply in some cases
As for the confirmation email indicating they were eligible, that is a mystery, but worth contacting United to hopefully get the expenses refunded!