To be honest I don't want to read the whole study but the first thing that jumps out is the terminology used.
This in particular:
Flu vaccines, according to the latest scientific evidence, achieve a 1 percent reduction in influenza symptoms
vs:
This means vitamin D appears to be 800% more effective than vaccines at preventing influenza infections in children.
Did they mean to say that VitD is 800% more effective in prevention influenza symptom? I would hope that an Immunosuppressive steroid is more effective in preventing symptoms...even more effective than a bunch of Metals and chemicals in vaccines...
So these headlines are really misleading, it should say symptoms not infections. Unless they did a viral study on each child after the test.