SwingDJs

I've been told that the rhythm in The Swan Silvertone's "Mary, Don't You Weep" has the swung rhythm shifted closer to the first beat than the second beat. To be honest, I don't really hear it, but what other songs is this true of?

I would say the bass and the "bass" vocal part lead the listener to the odd beats and the drums (brush on the snare and later, the clapping) leads one to the even beats.

How one hears musical accents is a little difficult to objectively define. Some people are used to listening to music in a way the makes one part more obvious (to them) than another. What anyone hears in a piece of music is very subjective.
I am amazed at what I learned to hear after taking music theory, Dalcroze (eurythmics) and motion study classes. And yet equally amazed when I see a really good dancer interpret the music so that I see something I hadn't heard before.
My girlfriend led bands in highschool and she constantly surprises me with things I think I would otherwise miss.