Your explanation couldn't be more wrong. Just by your definition, every position is a "need." The only understandable way to define drafting by need is when a team intentionally drafts to fill the one or two most glaring holes early in the order.
Heap wasn't a "need," but we knew that Sharpe was leaving/that we couldn't resign him after the season. You could call Reed a need in 2002, but we needed to restock a lot of defensive positions (a lot of folks then had Dwight Freeney becoming a Raven). You can't call wanting Leftwich drafting for need, because we grabbed the best player at the spot we were in then, too. Boller is borderline drafting for need, because Billick was so enamored with him as an overall player. You can say that we targeted Clayton, Ngata, and Grubbs in successive years, too, but that doesn't mean we drafted any of them based purely on need.
I don't think there's much merit in you denouncing the BPA philosophy, because the teams that tend to use it the most--and use it most effectively--tend to walk away with the best looking picks and best looking roster.