It can theoretically be sorted out if the ring is indigenous to the solar system or be an accretion ring centered around a mass other than the sun. If around another mass there should be a blue-shift of light that is approaching us and a red-shift from the part of the accretion ring that is moving away from us. If the ring is around the sun, no significant shifting would be expected from the sun's point of view.

Since the IBEX measures energetic neutral atoms, the main player would be gravity rather than magnetic fields. The fine structure could be a second independent example of Milgrom's predictions regarding possible solar system effects due to the EFE or external field effect. The first possible example was pointed out by Iorio with regard to the retrograde perihelion advance of Saturn. Milgrom suggested there also was a weak quadrupole effect where particles would be pushed towards a plane although it is not clear that this plane is the same as the ecliptic. The effect gets stronger as one gets away from the sun. These forces are very weak being a million times weaker than the Pioneer anomaly and a trillion times weaker than the flyby anomaly. So any magnetic field would dominate over this. But neutral atoms could manage to suffer from the force and crash into the plane after falling for a long time. The plane would be the hottest place and cooling as one gets away from the plane. This is the apparent profile of the fine structure seen by IBEX.

It does appear serendipitous that the IBEX and Saturn observations occur just on the heels of Milgrom's recent paper this past summer.

Indeed.

Have any detailed photographs been taken revcently towards the center of this plane? I have been wondering about DM 61 366. Same part of the sky as that star?

I am unaware of any other images than the IBEX. If the plane of neutral particles is close to the heliosphere they may make good targets just due to the density for spallation products. Could the PAMELA, ATIC, and FERMI excesses be due to cosmic rays ramming this plane of neutral particles and making the extra electrons and positrons? Would this preclude the need for Dark Matter Particle self-destruction scenarios?