Lemme just throw something out to get the ball rolling a bit.
We tend to think of coral skeletons as a taxonomically diagnostic structure. While a lot can certainly be gained at the species, genus, and family level from examination of the skeleton, there is strong evidence that the presense/absense of a skeleton itself is not diagnostic, meaning that the order scleractinia is not a true clade.
Instead of a single origin of skeletons in stony corals there seem to be several periods in geologic history when skeletons have emerged and disappeared within these sorts of animals. Thus, skeleton-producing corals (we're excluding hydrozoans, octocorals, etc. here as all of those groups clearly evolved separately and skeletogenesis arose separately) are not necessarily the descendents of a single group that began to calcify many millions of years ago. Rather, in the group or groups that led up to scleractinians the production of a skeleton varied over geologic time depending on seawater chemistry. During some periods the chemistry was appropriate to allow calcification and during other periods it was not. Over millions of years clades of anthozoans developed then lost then redeveloped then lost, etc. skeletons. It's clear that the capacity to do so remained intact (hence, redevelopment), but the actual production varied. The most plausible explanation would be that the genes involved in calcification were simply upregulated or downregulated over time, but probably not lost (or irreparably damaged).
This is particularly interesting today. Within the subclass zoantharea (6-way symmetry) we have 15 orders, 6 of which are still alive today. Zoanthidea (zoanthids), actinaria (sea anemones), ceriantharia (cerianthids, tube anemones), antipatharia (antipatharians, black corals), and ptychodactiaria (common name???) are all clearly physiologically different from scleractinians (stony corals) or corallimorpharians (mushroom polyps).
The interesting thing is, however, that physiologically corallimorphs fall right in with scleractinians, except that they don't calcify. They look, effectively, like "naked" coral polyps. Indeed, the "naked coral hypothesis" was proposed some decades ago to explain the apparent rise and fall of calcification over geologic history. The idea is as proposed above: that over time the critters either did or did not produce skeletons depending on whether or not doing so was feasible with the reigning seawater chemistry. Thus, it was hypothesized that many corals simply "went naked" by losing their skeletons when seawater chemistry made calcification unfavorable, and reverted to non-calcifying (or weakly calcifying) little anemone-like critters.
What would the general form of a non-calcifying coral polyp look like? Well, it would look like a corallimorph. Monica Medina's lab et al., took a genetic approach to this question a few years ago, and sure enough they found that modern corallimorphs are more closely related to one clade of scleractinians (including acroporids, pocilloporids, poritids, etc.) than they are to another clade of scleractinians (including Montastraea, Colpophyllia, Mussa, etc.).
So, it appears that the order scleractinia is truly polyphyetic. It includes two calcifying groups, but excludes a non-calcifying group that probably should be part of the clade. In order to fix that one would either need to split the stony corals into two orders, or corallimorphs would need to become part of the scleractinia.
There's no evidence that corallimorphs can calcify anymore, so they probably really have lost that ability at this point. It seems very, very likely that they are, indeed, naked corals.