The myth that comforting your child will "spoil" them is not only emotionally harmful for kids, its application actually creates an altered brain state that leads to higher levels of stress and mental illness in adulthood.
Neuroscience imaging has been able to correlate early childhood neglect and trauma with an enlarged amygdala.(higher reactivity) As well it has correlated secure attachment relationships with a thicker neocortex (better executive functioning).
So when your child is emotionally flooded, no matter if it is over a significant loss or something small, giving them compassion, proximity and comfort will only help them develop a healthier brain function and won't spoil anything except maybe someone else's perception of your parenting.
And if the choice is between your child's brain and someone else's approval...it's not much of a choice really.