Thanks, I forgot that bit of precedent. Checking a transcript, his words were "I just gave away ten years of my life." Sounds like probably a use of regeneration energy, though it's a bit ambiguous.

I do consider charging up the TARDIS as fundamentally different from healing a person, even if that person has special qualities due to her conception in the TARDIS. I also found that particular moment of Rise of the Cybermen to be a little dumb in the first place. Still, you are right that Eleven's healing of River's hand is not as completely out of left field as I initially believed.