With humans out of the equation, what could cause forest fire?
Wildfires are mainly caused by humans (or their technology) and lightning. Lightning is the most prolific natural source.  There really aren't many other sources in most areas, unless there is volcanic activity or a meteor strike as you mention.  There are also occasional cases of wildfire when peat dries out.
During a hot-dry summer, it can take several days of rain to moisten vegetation enough so that the fire danger is curtailed.  If there is a little rain accompanied by lightning, it is probably much less than what is needed to lower the fire potential (dryness of vegetation).  

Furthermore, lightning strikes are not "usually accompanied by rain".  In the Pacific Northwest, for example, there are several lightning-caused wildfires every summer in areas where summer rain is quite scarce.  This is discussed a little in Wikipedia:


  The term dry lightning is used in Australia, Canada and the United States for lightning that occurs with no precipitation at the surface. This type of lightning is the most common natural cause of wildfires. Pyrocumulus clouds produce lightning for the same reason that it is produced by cumulonimbus clouds.