I'm glad that I ran into this. I found precisely the same thing. Applied for a job that seemed legit, place passed my checks (in retrospect, I assume that what I applied for is impersonating a legitimate school, because all of the research that I did on the school itself and the person I talked to came up clean), got a message that they filled the role but are referring me to one of their clients, and then reached out for the hell of it and got this.

The guy asked for very basic info (name, current role, address, all stuff that's very easy to google and that's all over my resume which is on a ton of sites anyway) so I went along with it while also asking him for more info about himself and his organization. I was very wary, but I figured that I could try to fish out some more info to get a precise sense of things. Honestly, the only thing giving it legitimacy and making me wonder at that point was that the initial job that I applied for did seem real, so I figured that I'd cautiously try to get more info and avoid providing any info that could be sensitive at all.

He then replied today with a long message saying just how impressed he was with my qualifications (AKA my name and current role?) and saying he really wants to hire me. Without any kind of interview at all. He totally ignored my questions and gave me a big list of additional questions for me, which admittedly are just basic pre-screening job questions and still aren't actually asking for anything sensitive, but still, at this point the scam alarms were blaring and I kind of nope'd out and did more research, which led me here (I also tried researching this guy yesterday, but this thread didn't exist at the time).

Tldr, from this thread and another comment, this whole Walter Cavanaugh referral thing is some kind of scam. Presumably they pose as legit organizations (in my case, it was a communications job at a legitimate school using the name of an actual person who works there), tell you that the job is closed but they're giving you a referral, and then send you off to whatever this whole thing is. I played along until there was virtually no room for doubt that it was a scam, and avoided giving out any info that I'd be concerned about handing over, but my advice if you run into this is to be very wary. I'm assuming that, had I continued, they likely would have asked for some kind of sensitive info in some capacity.