I'm not sure this is correct. The projected image won't get any wider regardless of the image format without physically zooming in/out. You tell your projector (usually in an on-screen menu) in its initial setup what your screen ratio is, then it adjusts the output accordingly. Like our 16:9s add black bars to the sides for 4:3, a 4:3 output will just add the bars to top/bottom for the 16:9, with the width staying the same.
So to get back to your re-worded question, no, there's no reason you can't watch 16:9 material on a 4:3 screen. You just have to deal with the black bars. I think if you only partially lowered your screen to fit the 16:9 dimensions, then you'd have to physically adjust the aim point of your projector (lens offset) because it would no longer have the same center.
So yeah, I guess going with a 4:3 screen would give you the maximum image for all aspects, but you should consider the room setup. At the dimensions you give for a 4:3 screen, that's a 140" diagonal, which means you'd have to be sitting pretty far back to get somewhere around the THX-recommended distance (see the other recent posts on this). And your projector might have to be pretty far away to have an image this large, which means it may not be as bright. And again consider your viewing habits. We hardly watch any TV on ours, so I love having the DVD images fill the whole screen, while it doesn't bother me to have the TV images a bit smaller for the rare times it's on. It's an aesthetic thing (and keeps my wife from asking why we always have those bars with this big screen!). Just some other things to consider.
Cheers,
Kevin