I agree with you, Josh. "Web" is not a lead source. We collect similiar information, but with only four data points:
1) Date
2) Channel (i.e. Social Media)
3) Channel Details (i.e. LinkedIn)
4) Content
And, of course, the "Who" information you mention. Sometimes even those four fields are more than we need. If we need more detail, we can add it to the "Channel Details" field. So in your example, it would be:
1) Date
2) Newsletter Ad
3) Magazine X
4) Webinar Y