They enrich the standard model by assuming that unions do not only care about their members' wages, but also about their health. Because workers cannot precisely judge the effects of working conditions on their health--an information asymmetry--, competitive markets cannot provide an efficient solution, leading to low standards (standards are costly), to more accidents, and to inefficent high sickeness levels. (Without information asymmetry, workers would require higher wage rates, resulting in compensating differentials.)
If unions are better informed than their members, or, alternatively, invest resources into the analysis of workplace hazards, they will bargain for better health and safety standards. This will ultimately result in healthier workers and lower absence rates. (The union "internalises" at least some of the externality arising from information asymmetry.)
So far, exciting stuff! However, as often in this type of research, there is almost no data available to test this empirically. They make an heroic effort to interpret union densities across countries in the light of their theory, but they conclude with an appeal
"It might be a good idea for unions to go and collect data on these issues." (p1008)
To which I'd like to add: I'd love to analyze these data!