Even in rain on the BC coast I was able to find tinder under outcrops of rock and on the dry sides of cedar trees.
It does not need to be much of an overhang to keep something out of the rain.
Cedar bark usually is dry on the side of the tree and can be shredded enough to catch a spark.

I have also found that grasses can usually be found either growing against something or under a tree sheltered enough to be dry.

I have raided rodent nests for tinder just to see if it worked, and it did. Mice and squirrels shred the tinder for you.

Doug mentioned cat tail heads and that stuff catches like gasoline.
Thistle down is good too.

Some of the lichens can be used, like Usnea species, but I never had much luck with them when it was wet out.

I have had a harder time finding tinder when it is fog and dew than just rain. I am usually looking for stuff sheltered from the rain when I am looking for tinder and foggy dew goes everywhere.