There's no claim that health was correlated with the presence of trees.
From the summary of the article::
'Well my basic hypothesis was that trees improve people's health.
Yes - that's the hypothesis, but the evidence to support it doesn't come from an observed correlation between trees and health, as previous people have said that would be confounded will all kinds of other factors which would be impossible to measure. The evidence comes from the observed correlation between the pest and health, which is presumably (and this is big assumption) not confounded with other factors, with the presence of trees as the only possible mediating factor.