Bleed damage cancelling fire damage out?

I had it several time now that a fire dot wouldn’t work. I suspect that bleed dots cancel out the fire dots. For example: I hit an already bleeding Arthron with a flamethrower. He took some fire damage. However, in the AI turn only 10 bleed damage was applied to the Arthron, but not the fresh 40 (- 20 armor) damage fire dot (the Arthron had only 20 armor max).