I don't see how willfully blending these two things is helpful for anyone. In this context, it can be safe to assume that everyone knows this technical distinc

I don't see how willfully blending these two things is helpful for anyone. In this context, it can be safe to assume that everyone knows this technical distinction (even for those of us who are not web programmers). In other contexts with less computer-technical people, I don't think being annoying and correcting every "technically incorrect" mention of "The Internet" when they mean The Web is helpful. But I think it is helpful to remind them of the distinction if you are actually talking about the subject (as opposed to just saying things like "look at your internet, I just sent you a facebook message"). Computers are magical enough as it is; it doesn't help anyone to make it even more so when they are even slightly interested in discussing some part of computing or IT. Explaining that The Internet is the infrastructure and the Web is just one the things that uses this infrastructure seems simple enough to grasp, and isn't an oversimplification at all. People understand that the electricity grid has to exist in order for them to make toast.