Well, I've got access through the university. It's not much. Basically, child cycling injury rates have been decreasing in Sweden, especially in Kristianstad and Skaraborg. Helmet use has been increasing, as has ridership and infrastructure improvements (separated cycle lanes, etc). The authors suggest that of all those three factors, helmets are the most likely to have reduced injury rates.
They uncritically cite the Australian mandatory helmet reduction in fatalities and Rivara et al (1994) in their conclusion, but really they don't provide much, if any, support for their contention that helmets are the only (or even major) factor in reducing head injury rates. They're focused on children's injuries, which may not be indicative of the value of adult helmet wearing, and their argument also appears to be falling into the trap of Thompson and Rivara (1989), where cycle helmets somehow prevent non-head injuries.