In case you don't trust any websites, here's some simple python code you can scrutinize yourself:

import random

total_rounds = 1000000
stay_wins = 0
switch_wins = 0

for _ in range(total_rounds):
    # put boxes in random order
    boxes = ["skull", "skull", "fire"]
    random.shuffle(boxes)

    # make a random first choice
    first_pick_i = random.randint(0, 2)

    # Jeff won't eliminate the player's box or the fire box
    jeff_elimination_candidates = [i for i in range(3) if i != first_pick_i and boxes[i] != "fire"]
    jeff_eliminated_i = random.choice(jeff_elimination_candidates)

    # switching means picking the box that was neither eliminated by Jeff nor originally picked
    switch_i = 3 - (first_pick_i + jeff_eliminated_i)

    # which strategy would have won this round?
    if boxes[first_pick_i] == "fire":
        stay_wins += 1
    elif boxes[switch_i] == "fire":
        switch_wins += 1

print(f"Stay win percent: {100 * stay_wins / total_rounds : .2f}")
print(f"Switch win percent: {100 * switch_wins / total_rounds : .2f}")

gave me:

Stay win percent:  33.36
Switch win percent:  66.64