It says that it is cooling in the stratosphere is consistent with ozone depletion, not that ozone depletion causes cooling (although this may be the case). Of course, the next sentence is ...
In addition to the recent cooling [stratosphere or troposphere?], large temporary warming perturbations may be seen in the data due to two major volcanic eruptions: El Chichon in March 1982, and Mt. Pinatubo in June 1991.
Hey. If their reasoning can be sloppy, so can mine! :)