I think the OP is right, at least in so far as what we think Uriel did in Small Favor was not what he actually did, or at least not exactly what he did. I've suspected that since Mab, at the end of the book, told Harry that only he would be able to answer the question of what exactly Uriel had done to him.
At the end of White Night, Harry discovered that Lash had left him a gift of knowledge in the form of musical talent. Presumably, Lash's musical talent, made a part of Harry's mind when Lash took the psychic bullet-- either by Lash's design or by chance. Serack's theory may be entirely correct, and the knack for Soulfire was also a gift from Lash, and Harry just didn't realize he had it until Uriel bumped his metaphorical elbow. Even if the truth isn't quite that direct, though, I'd guess that something of Lash's knowledge or mind did give Harry a vital piece of whatever is required in order for a human to use Soulfire.
At any rate, I think that, whatever it was Uriel did, it was something to do with Lash or Lash's remnants. And a direct side-effect of it was to give Harry access to Soulfire. I suspect it also had something to do with the way Harry's left hand was able to dextrously snatch the denarius out of the air before it could touch him, in SmF, too. "The burned hand teaches best," was the first quote Harry saw when he opened Uriel's copy of The Two Towers. Maybe Uriel did something to help Lash put herself back together, intending that Lash should become Harry's future teacher.
If that were true, though, I have no idea why she wouldn't have popped up by the time of Changes. When Harry mentioned the headaches at the beginning of Turn Coat, I thought for sure that was a sign of life for Lash, but between TC and Changes, the headaches apparently vanished. And still no Lash. So who knows? Maybe the headaches were something completely different.