There's your problem, dollars to doughnuts.

From your photo, I can see that the faces of the "bolts" (nuts, actually) are sticking up clear of the chainring instead of flush with its surface as they should be. The 5 mounting holes on a chainring are countersunk on the inboard side, to allow the nuts to nestle down into the chainring to prevent exactly your problem. I suspect that someone has flipped your inner ring over, perhaps to get a few more seasons' wear out of the teeth. Suggest you remove the inner ring and re-install it with the countersunk side inboard. You can do this without removing the crank -- usually you don't even have to remove the pedal. If you find that for some reason your chainring does not have countersunk holes on one side, get one that does.

(You don't want to remove the crank because each time you re-install it, you enlarge the mounting hole a tiny bit, making it drive farther inboard on the spindle.)

Putting a spacer under the fixed cup is not exactly easy and painless: the fixed cup is a bugger to get out usually. (Not for nothing are they called "fixed".) Before you start down that road, make sure there is at least 1-2 mm of the adjustable cup sticking out beyond the lock ring now. Otherwise after you've gone to all that trouble putting the spacer on the fixed side you'll find that the adjustable cup disappears all the way into the bottom bracket shell leaving no threads exposed to engage the lock ring. Grrrrrr! (In a properly spec'ed bottom bracket, the lock ring will already be flush with the adjustable cup as is. Unlikely will you have extra threads showing now.)

But get those chainring nuts flush first. They absolutely should not sit proud of the chainring.

Les

P.S. Why should only 3 of 5 nuts rub? Are you sure the ring isn't warped?