Putters that actually sit SQUARE!

I too have a Scotty SS Newport 2.5 and have just tried this on a vinyl floor that has an embossed tile effect. Lined up the face against one of the lines, released my grip and hey presto..... face stayed square!

However if moved my hands forward a bit the pivot point on the sole changed and the toe opened slightly, which is what I'd expect from a "toe heavy" putter. In fact the same happened with my Odyssey Rossie which is face balanced. Of course the face on that wants to swing open too but only so it faces the sky when the shaft is balanced horizontally.

No doubt some complex physics, geometry and mechanics involved but intrigued as to why yours looked shut. Might be worth trying it on a flatter surface and see what happens if you raise lower the toe or move the shaft forward or backwards.