They're not really exclusive ideas. The Constructor Injection section in Fowler's article is exactly the same as the Strategy pattern. But no one talks about the Strategy pattern anymore, it's all wrapped into the idea of DI and that's what caught on.
It was interesting reading this exchange. I have a similar understanding of DI to you. I have never even heard of a DI framework and I have trouble picturing what it would look like. It was interesting to watch you two converge on where the disconnect was.