There was, from what I could tell, some debate at the time on what Dust Bowl Willy was. Many people, especially those who weren't very familiar with newspaper comics from the 1930s, hadn't heard of it. What they didn't realize was that people who were very familiar with newspaper comics from the 1930s hadn't heard of it either. Dust Bowl Willy never existed. Darby Conley simply made it up to sound like a comic strip that might have come from that time period.
I'm not sure if Conley was deliberately using a fictional strip to amplify some of the themes and ideas he had seen in period strips, or if he simply didn't want or wasn't able to do any substantive research to use a real strip. In either case, he utilizes his strip to comment on how language and humor are tied to culture, and that culture can shift and change over time even if it remains geographically static.
What's interesting here is that Conley has been criticized in the past for falling back on re-run strips without really telling anyone he was doing so. Re-run strips began appearing with greater regularity around 2011 and, by 2013, the daily strip (excluding Sundays) was entirely old material. Which means that this "Dust Bowl Willy" storyline that is commenting on how culture can shift over time is becoming itself increasingly dated.
"Ha ha! Remember this strip and how we had that long conversation on Usenet trying to figure out if Dust Bowl Willy was real?"
Yeah, I actually dug up an old Usenet thread discussing exactly that.
Irony, thy name is Darby Conley.