Lyle et al. (2007), prior to the paper you mention, also came up with this idea that the ACC initiated with its modern setting (i. e. with strong currents and mixing throughout the water column) during the Late Oligocene (ca. 25 Ma), so roughly 10 Myr after the Eocene-Oligocene when the antarctic glaciation is thought to have occurred. Their evidence is based on sedimentology, specifically the presence of erosional structure associated with deep current flow. They however don't discard in this paper the idea that a surface ACC existed prior to this.
The original idea (Kennett 1977) according to which the ACC started near the Eocene-Oligocene transition was based on the observation of biogenic sedimentary facies pattern (classically siliceous south of the ACC and carbonaceous north) coupled with the observation of the opening of the Drake Passage around that time. Later, observations of the establishment of an endemic antarctic planktonic fauna during the latest Eocene (e. g. Lazarus & Caulet 1993, Lazarus et al. 2008) and measurement of Nd isotopes (Scher & Martin, 2006) at Agulhas Ridge (i. e. south of Africa) that coincides with Pacific waters values strengthened that hypothesis.
However, the idea that the antarctic glaciation was a consequence of the setting of the ACC has been somewhat challenged (De Conto & Pollard, 2003, and later Barker & Thomas, 2004) based mainly on numerical modeling, as they show that, although a developed ACC would have participated in the cooling triggering the glaciation, it is not a necessary condition for it: the glaciation could have entirely been caused by the observed drop of atmospheric $p_\mathrm{CO_2}$, even without a developed ACC.
Additionally, some of the evidences for an early setting of the ACC (namely the facies change argument) could very well be a consequence of the glaciation rather than the consequence of the ACC (Barker & Thomas, 2004).
So, as far as I see, we are at a stand-off, where we have arguments in favor of a late settling of the ACC (mostly sedimentary and tectonic arguments) and at the same time arguments in favor of an early settling (in particular paleontological and geochemical arguments) and no real reason to discard any.
References:
Barker & Thomas, 2004. Origin, signature and palaeoclimatic influence of the Antarctic Circumpolar Current. Earth-Science Reviews, 66: 143-162.
De Conto, R.M., Pollard, D., 2003. Rapid Cenozoic glaciation of Antarctica induced by declining atmospheric $\mathrm{CO_2}$. Nature 421, 245 – 249.
Kennett, J.P., 1977. Cenozoic evolution of Antarctic glaciation, the circum-Antarctic Ocean, and their impact on global paleoclimate. Journal of Geophysical Research, 82: 3843–3860.
Lazarus, D. B. & J.-P. Caulet, 1993. Cenozoic Southern Ocean reconstructions from sedimentologic, radiolarian and other microfossil data. In J. P. Kennett and D. A. Warnke (Eds), The Antarctic Paleoenvironment: a perspective on global change. Antarctic Research Series, 60: 145-174.
Lazarus, D. B. et al., 2008. Patterns of opal and radiolarian change in the Antarctic mid-Paleogene: clues to the origin of the Southern Ocean. Micropaleontology, 54(1): 41-48.
Lyle et al., 2007. Late Oligocene initiation of the Antarctic Circumpolar Current: Evidence from the South Pacific. Geology, 35: 691-694.
Scher, H. D. & Martin, E. E., 2006. Timing and Climatic Consequences of the Opening of Drake Passage. Science, 312: 428-430.
