No, the white man intentionally brought smallpox among the Indian Nations. He was immune.
Some historians have made much of an incident in Pontiac's rebellion in which Fort Pitt was besieged. There is no doubt the Indian intent was to slaughter every person in the fort, save whatever few they might fancy to take as captives.
During a parley with the attackers, a British officer handed the Indian representatives two blankets and a handkerchief thought to have been exposed to smallpox, in a desperate gambit to break the siege and save the lives of those inside.
The gambit in fact failed, as the Indians outside who kept up the siege were apparently unaffected by disease a month later.
Nevertheless, many Indians in attacks on other locations did contract the disease and spread it in their villages when they returned. This outbreak of the disease predated the blanket-giving incident at Fort Pitt. It appears that as the Indians in these other locations were slaughtering their victims (an up-close and personal activity), during this contact they contracted the disease. So some of these Indians thus got their just desserts.
White men immune to smallpox? Not by a long shot.
"Less susceptible", perhaps, but by no means immune.
Smallpox vaccination was not developed until 1796, by Edward Jenner.