The Goddess Scorned, Bleeding and Burning

I just found out that the bleeding debuff inflicted by Puncture doesn't deal any damage when you're using The Goddess Scorned. This might actually not be a bug since the sword has a mod that says "You can only deal damage with this weapon", but I still wanted to bring it up because it struck me as odd.
Burning damage over time of course works just fine, that's kind of the whole point of this weapon. But from an ignorant player's point of view burning is the same thing as bleeding damage over time, just in fire form. So why would one thing work and the other would not? Is this because the burning effect is actually internally triggered by the weapon itself and the bleeding effect is technically triggered by the gem?

Of course, that makes sense. Thank you for clarifying this Roman! I wasn't really sure how this worked, so I guess the reason for the sword dealing physical damage in the first place is to let you scale the base damage with physical-% nodes and have that multiplied damage converted to fire afterwards?
It's still a little irritating that the bleeding effect would show even though 0 damage is dealt. The same thing probably happens with Immortal Call, I haven't tested it though. Maybe it could be made so that the effect will only show when actual damage is applied?

Edit: Some more thoughts added to expand on the original question.