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I wouldn't bank on it being stiffer...the bottom bracket is where you need the most stiffness....so that is where you want the most support. Normally all the tubes converge there, giving the stiffness from the triangulation of the back end.
Having the BB in the centre of the tube will decrease stiffness.
The more open rear triangle will be far more flexible, as smaller and tighter triangles are stiffest.
I'd be very surprised if adding a second triangle by using the skinny mid stays would make that back end stiffer than a regular diamond frame.
The BB having no chainstays mounted either side behind it means it has nothing to stop the twisting forces that pedalling would impose on it.

I agree with you about getting stiffness from the small triangulation in the frame, but I think that the extra lower stays combined with the higher stays would definitely increase stiffness laterally.
It also looks like the BB is set off the downtube, so that there is no compromise in that tube nor the join to the seat tube, in fact it probably has a significant piece of lugwork down where the BB is.

I'll send the picture to my Dad, he's a keen cyclist from that era, and a structural engineer he may well know what the reason for the design was.