Confused about adding innate attacks to weapons

[theotherscott]

There seems to be a discrepancy in cost when adding an innate attack to a ST-based weapon compared to an unarmed strike.

Per the FAQ, adding fire damage to a sword may be priced as follows:

12 points:
Burning Attack 3d [15] -20% (Melee Attack, reach 1 -25%; Link +20%; Accessibility (wielding a broadsword) -15%)

Even though a sword is a ST-based weapon, the FAQ specifically notes to not add (Melee, ST-Based +100)

Defining the attack as a follow-up to a single weapon is about the same cost:

12 points
Burning Attack 3d [15] -25% (Melee Attack, reach 1 -25%; Follow-up +0%)

However, try to add damage of some sort to an unarmed attack, you have to add the (Melee, ST-based +100%) modifier. Adding 3d crushing damage to unarmed strikes costs:

26 points
Crushing Attack 3d [15] +70% (Melee Attack, Reach C -30%; ST-Based +100%)

Why the point difference? What logic is there for required a +100% modifier for unarmed attacks but not ST-based weapons?

Also, how would you add burning damage to an unarmed strike?

EDIT: Meant to write "3d" instead of "2d" for the crushing attack.