The creature that's holding the object that's the target of the spell burning disarm does have a choice
The creature holding the object affected by the spell burning disarm can either...
- Choose to make a saving throw against the spell burning disarm.
- Success means the creature drops the object targeted by the spell right now and the creature isn't dealt damage. Normally, a creature can only take free actions (except speaking) when it's the creature's turn. Success on this saving throw allows the creature to drop the targeted object even when it's not the creature's turn. (Such an act usually takes a free action.)
- Failure means the creature retains its grip on the targeted object and is dealt damage.
- Choose not to make a saving throw against the spell burning disarm. The creature retains its grip on the targeted object and is dealt damage.
Although it seems strange to succeed on a saving throw to drop the targeted object, doing so when the object's affected by the spell burning disarm spares the creature holding the object damage from the spell. Usually, avoiding damage is a good thing; in this case, however, being disarmed may be worse, so the spell allows the victim a choice, albeit a sort of Hobson's choice.
Neither failing the saving throw nor choosing not to make a saving throw prevents the creature from dropping the object normally on the creature's turn. (Bear in mind, though, that the duration of burning disarm is instantaneous, so there's no reason to drop the object subsequently unless fearing further burning disarm spells.)