The Org. Lett. paper by Michiko Sasaki and co-workers from Japan contains a reminder of how unusual N-phenyl-1,2,4-triazolinedione (PTAD) is as a dienophile. PTAD is one of the most reactive participants in the Diels-Alder process described to date; attempts to understand its reactivity date back many years. If you are keen to find out more about the strange behavior of PTAD in Diels-Alder reactions, I would recommend the 1998 paper by Houk and co-workers:
http://pubs.acs.org/doi/abs/10.1021/ja982050y
The extreme characteristics of PTAD are seen, for instance, in how it reacts with dienes that cannot easily adopt the requisite s-cis conformation. PTAD engages these molecules, leading to products of 1,4-addition – and this is just one of the pathways that were examined by Houk. Coming back to the Sasaki paper, I liked the comparative study with N-methylmaleimide (NMM): the reaction between one of the allene-containing silyl enol ethers and PTAD goes smoothly at -80oC, whereas NMM clearly does not have “enough” in it even at room temperature. Those adjacent nitrogen lone pairs… Pure magic.
amphoteros 
the same problem as with DEAD, only more so: it is a such a good oxidant it will happily take one electron at a time, in which case you don’t necessarily get a concerted TS.
This is demonstrated in reaction of DEAD with styrenes: you get o-substituted phenylhydrazine derivates. In the case of styrene they are cyclic, (formal DA product) but with alpha, beta methylstyrenes the main product is acyclic (product of formal ortho CH insertion to DEAD, with subst-vinyl substituent intact)
You are right, DEAD is another one of those strange beasts…
Could PTAD also be acting as a diradical? I have several examples where I used PTAD to remove conjugated dienes and it ended up reacting with skipped (1,4) dienes as well.
I think so, definitely some possibilities there.