The authors of the study state that employees with paid sick are less likely to be involved in a work-related accident than employess with without it. They also state that highest-risk occupations showed the highest dicotomy between paid and unpaid leave.
There are some flaws in the hyphotesis though, as we don't know some important details about the study.
First of all the authors do not state the jobs taken into consideration in the study, or at least the different types of them. Did they take into account only high-risk and fatigue works such as construction? This detail is important because a worker may not be able to carry out his own work at all if he is ill, since his work would need great physical conditions and good shape.
Doctors and nurses for example are required to be in good physical conditions as they have to get in contact with sick people.
Then the authors do not state the money condition of the people involved in the study. Presumably these people are medium or low income workers and therefore the can't afford a no-salary period.