Agreed. I'd be very surprised if that '61 was originally sunburst. Most likely blonde. But the old adage "never say never with Fender" might apply here. There have always been factory outliers, not to mention that Fender was open to special order requests, even in the 50's. A Fender dealer requests an ash body with a sunburst finish?...sure, why not.
Regardless of the reason for the dark edges on the body (previous refin?...previous finish burned off with a heat gun?), I'd have the body professionally "restored" to an era-correct blonde. And I'd have it (I can't believe I'm saying this) relic'd to match the play wear on the neck. The bass has more than enough value to justify the cost of restoration. In for a penny, in for a pound I say. YMMV, TETO, etc. Cheers.