If it's a scam, I doubt it's the seller's scam. If he wanted to scam people, he'd put SIGNED BY CLIFF EDWARDS in the title. As it is, someone interested in an Edwards-signed item might well not find this. Pretty inept scamming, if you ask me.
Is it possible that someone else (other than Edwards himself) put Edward's signature on that uke at some point? Sure, it's possible. I put Pete Townshend's autograph on one of my Who albums when I was a kid. I wasn't trying to scam anybody, it was for fun. But I suppose someone might put their hands on that album some day and assume Townshend had signed it, not some 12-year-old wannabe.
The linchpin for me is that it's an accurate signature. Since there's little clear evidence of scamming, and its too good to be random, I believe it's the real deal. Since there is no provenance, its value as a signed item will always be limited, but for someone who wants a good quality uke with the special plus of a likely-to-be-real Cliff Edwards signature, I think this is a good deal. Plus, how much do you love that case? I love it a lot.
If I hadn't just bought one of my "holy grail" ukes this week, I might go for this. As it is, one of you other crazies will have to pick it up...