The species can be distinguished by its slightly-flaring, mildly-ribbed, tubular involucres with 5 apical lobes each bearing a long, straight, narrow awn. Each involucre contains 4-6 short-pedicelled flowers which open in succession, each one with 6 entire perianth lobes. Opposite each involucre is a one-sided bract with 3 triangular lobes, each with an apical awn. With the long, straight, and narrow awns of its involucres and bracts, it strikes me as more Oxytheca-like than Chorizanthe-like (note in addition that Oxytheca usually have numerous flowers per involucre whereas Chorizanthe have a single flower per involucre).

Dylan Neubauer provides a very informative discussion of Aristocapsa insignis, which includes info on the taxonomic history of the species. Here are links to some of the references cited there, in reverse chronological order: Reveal & Hardham(1989); Goodman(1957); Abrams & Ferris(1944) (see also figure '1336' here); and Goodman(1934).