The declaration of MustUse::health_check_troubleshoot_theme_stylesheet() should be changed to allow bool in addition to string for both the $default param and the return type.
This is because this method is hooked into pre_option_stylesheet, which passes false as the default value to the filter. Core's get_option() checks returns early if the return from the filter is not false (strict comparison) and, thus, doesn't even check for the DB value of the option.
Note: the change I'm suggesting is the way the MustUse::health_check_troubleshoot_theme_template() is declared.