I'll try to make this explanation simple - it's a bit of a puzzle.
A client of mine asked me to make the bg image on a site 'a little bit darker', so I did 4 versions. I made 3 copies of the original style in the stylesheet:
I was thinking that using an inline style for that property might slove the problem. Does that sound reasonable?
Sorry, but that has nothing to do with it and won't do a thing.
On any Mac from the last few years you would likely use Safari (or FireFox or Opera or Camino or...there is not just one generic Mac browser that somehow has problems unlike Windows), which is the default browser.
The backgrounds appears (all of them) in Safari, on any modern Mac.
The user with "trouble" viewing the background may be using IE for Mac - they should not - it is not supported by M$ or Apple in any way - it is a dead browser that should not be catered to.