The towers were draped in fresh animal hides, not dried pelts. "Fresh" skin is resistant to burning, much more so than wood - even when the wood is damp.

The Tyrians eventually decided to sabotage the two siege towers with a fireship, loaded with combustibles like sulphur and pitch. The large amount of material, and the ship itself caused enough damage to destroy both towers. The animal hides couldn't protect them from that much direct, constantly applied heat.

Source: Battles that changed history, Amber books ltd.

I'd like some real evidence that fire arrows were ever effective at anything, especially in these past ages of non petroleum based flammables. I believe that they are mostly a myth.