...Except the datasheet does clearly states a 2uV p-p max noise, does it not? Which is what Andreas' part is doing, and I would say is operating properly - at least from the graph shown. The datasheet doesn't distinguish the "type" of noise, but you do get a boundary limit. That 2uV p-p limit is still <0.3ppm p-p on a 7.15V scale, and difficult to measure accurately especially as a real -absolute- value change.
That noise level is also in the realm of contributing binding post thermals, air drafts, EMI and lots of other causes outside the LTZ can.
DigilentMinds was referring to something I think operating farther -outside the bounds- of the datasheet limits, and that's something that piqued my interest. From what I've seen that doesn't happen often with LTZ's (on proper PCB, proper draft protection, noise shielding, etc.), and I was curious about the date codes of those parts involved, if known.