You are correct. The exclusion of damage done by birds, vermin, rodents, or insects does not apply in this case. This exclusion is meant to eliminate coverage for damage by birds, etc. that occurs over a period of time. For example: pigeons get into an attic and live there, building nests and doing damage over the course of several months—that damage is not covered.

 The exclusion of damage by birds, vermin, rodents, or insects is included in a longer list of things that occur over a period of time—such as wear and tear, marring and deterioration. According to Black's Law Dictionary (Fifth Edition), the principle of ejusdem generis says "where general words follow an enumeration of persons or things, by words of a particular and specific meaning, such general words are to be held as applying only to persons or things of the same general kind or class as those specifically mentioned." Further, all items in a list must be read in the same context.

 The damage done to your insured's home was sudden and accidental in nature. That is why one buys insurance. This claim is analogous to a household pet's causing a fire by knocking over a lighted candle. No insurer would deny the fire damage to the dwelling based on the animals exclusion.