The way it's used (by Brits exclusively I believe) is:

"He was sat comfortably on the sofa reading when he heard a sound", "I'm sat in bed when the phone rings", "She was stood waiting for hours", etc.

(So it's not just 'sat', but I'm not sure if it goes beyond 'sat' and 'stood'.)

But yeah, it does have an odd quaintness that suggests there could be a peculiar story behind it...