While hot water is effective as initial treatment, for stonefish venom, just pouring hot water over the stings does nothing.
Submersion in 45°C water, for 30 mins is necessary, followed by the antivenom if possible, and large amounts of painkillers.
As well as the excruciating pain, breathing difficulties, heart damage and nerve damage, stonefish spines can also cause infection and gangrene severe enough to require surgery.
Just pulling out the spines and giving the area a warm wash will have little to no effect.
It is not possible to just carry on as normal after being stung by a stonefish.
The paralysis or convulsions, agony, heart problems and inability to breath tends to slow people down. Leaving the spines in and the stings untreated would have lead to death long before Sam and Callen arrived with their handy knowledge.
Had the agent survived the stings, she wouldn't have been capable of even desk duty for weeks afterwards. It's not possible to just shake it off and push through.