How to address a slow garage roof leak
The ridge vent can allow driving rain in, but for it to be showing water damage, it would have to be getting in during nearly every single rain.  Is this area of the garage perhaps where the driving rain comes in or is there possibly something that cannot be seen in the pictures that would be directing more than normal water in?  

I don't think the tar paper is supposed to bridge the ridge like yours is.  I can't seem to find an install guide online at the moment, but last time I installed ridge vent, we did not have tar paper across the opening and the roof has no water.  I wonder if the water is getting on the tar paper and is getting through a nail hole causing this issue.