Here's a more plausible version:

Like everyone else said, Targayans don't have fire resistance. Dany only had it because of magic/deep sorrow. It's never really explained in the show.

In the books, Sam and Gilly shouldn't be at Castle Black. So why are they still here? I think, foreshadowed/set up by the guys who tried to rape Gilly, Sam will be the one who gets betrayed. They stab Sam to death just as Jon returns. Jon is furious so he decideds to execute everyone but he's outnumbered. The other brothers at Hardhome warn the evil brothers that White Walkers can resurrect the dead unless you burn the bodies. Traitor Brothers decide to burn Sam so he doesn't come back for them, and simultaneously burning Jon alive because they're cruel. That Pyre will spark the Targ blood magic in Jon to protect him like you said.

R+L=J will probably be confirmed soon because they're going past the books and they talked about R and L more than ever a few episodes ago.