Re: The magma's several km deep
Actually pressure differences are not going to be equivalent to the water column of rainfall. In volcanic systems any water that infiltrates (and doesn't runoff in a river or evaporate) is going in to fractures. Thees fractures are going to be quite small, so adding a metre of water at the top of the system may easily raise the water level in a fracture by 20 metres. Even in the UK some water tables fluctuate more than 50 metres vertically in a season (in extreme cases).
While the pressure change might still be small, it can still be the straw that breaks the camel's back - if you imagine pressure building up in the magma chamber linearly a small change in the system can be a trigger - without the rain an eruption would probably still happen - but maybe not for a few more months or years.