Sometimes it could be hard to define what type is a cloud above your head, and when looking on the photo it is even harder.
Indeed, with a photo the sense of scale is often missing.
But cloud classification is not a precise science anyway. There's a continuous spectrum between e.g. altocumulus and cirrocumulus; sometimes it's really clear as to whether a particular cloud formation is one or the other, sometimes it isn't.
All you need for iridescence is for the cloud particles to be small and of a very uniform size - this is really an indication that the cloud is either forming or dispersing (or sometimes both, on the opposite sides of a lenticular formation) and in these conditions the visible indicators of cloud type (like shadowing in altocumulus) are often missing.
The cloud formation with iridescence which I photographed (above) was quite definitely altocumulus though of an unusually thin and transparent kind.