The only detailed account we have of Baby-Skye's rescue from China (at least until Raina started talking about monsters recently) is from the guy that Coulson and May track down in "Seeds". He and Linda Avery were still rookies, and were part of the backup team, called in once the first response team was massacred (presumably by whoever was after the baby, not by the baby herself). They found the senior agent, who had originally called in the 0-8-4, hiding under a bridge, but dead. He had been either shot or cut in the neck (I forget which) and had "bled out" (not burned), but the infant was still alive. No powers were ever seen being used.
When Garrett and Skye first meet (in the episode with Nash, just after Skye was given her badge) they get to talking about painful wounds, and he shows her his third degree burns on his neck. There was some speculation at the time that this might have been due to his being involved in Skye's rescue, but this was nowhere hinted at in the show -- a 3rd degree burn is much different than bleeding out. Furthermore, a past-Garrett, who had no reason to lie, explained his wounds to Ward as being caused on a different SHIELD mission (I forget the details, but it was clearly not in China, or the result of a fire-baby), which ultimately caused him to join HYDRA.
These two events are unrelated (at least until proven otherwise... #itsallconnected).
EDIT;
Okay... lol, I guess.
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