Well this is all very interesting to me. I read the Peter White chainring page. While I agree with what he says, I also agree with what he does not say, which is that a 9 speed Ultregra triple FD works perfectly with a 52-39-26 combo. This is on my FSA crankset. Perhaps different 9-speed cranksets have different chainring spacings? Doesn't seem reasonable to me, though.

I dug out my collection of inner rings. They are all flat plates, no fancy features, because they don't need fancy features. The chain simply drops on and is lifted off by the next ring up. Some have counterbores on the inside for the chainring nut, some don't. Some are thicker on the inside for some reason and have deeper counterbores to compensate. They all have more bevel on the teeth on the inside than they do on the outside. IOW their teeth shapes are all the same. The Shimano rings are simple flat plates just like all the others.

Looking very closely at my setup, there is very, very little clearance between the chain on my 26T and my 39T ring, but it doesn't rub. OTOH with my FD set up the way I like it, while in the inner ring my FD cage rubs on the chain in any cog smaller than my 4th from largest. As I say, I'm not running the stock 9-speed 42T middle ring, since that would be a 16T shift from the 26, which seems a little large. Be that as it may, the Shimano and FSA stock 9-speed 30T inner rings are simple flat plates.

So I don't see how the chain on the inner ring can rub on the middle ring on some bikes but not on others, unless there is a difference in the crankset spacings. Perhaps someone can explain.

I suppose it's also possible that the OP's middle ring is badly burred and that's the problem. The middle rings on my tandem crankset don't seem to last as long as those on my singles. They get burred or the pins break off and I toss them. I suppose it's also possible it's a chain problem. I run nothing but Shimano Ultegra 9-speed chains.