The authors suggest this happened during a former period of high obliquity.
But there is increasing evidence these flows can happen currently as liquid water brines:

Title: Metastability of Liquid Water on Mars
Authors: Hecht, Michael H.
Journal: Icarus, Volume 156, Issue 2, pp. 373-386 (2002). (Icarus Homepage)
Abstract
A simple model of local heat transport on Mars demonstrates that transient melting of ice may occur in depressions and gullies nearly anywhere on the planet where thin ice is illuminated by normal-incidence insolation. An experiment has been performed to confirm the model of evaporation rate at low pressure. Reduction of radiative cooling due to gully geometry is shown to be important. Since appropriate meteorological, topographic, and optical conditions may occur on slopes nearly anywhere on the planet, hydrological features such as gullies would likely form only where such ice might accumulate, notably in sheltered locations at high latitudes. It is suggested that cold-trapping of winter condensation could concentrate a sufficient amount of ice to allow seasonal melting in gullies.

On the possibility of liquid water on present-day Mars.
R.M. Haberle, C.P. McKay, J. Schaeffer, N.A. Cabrol, E.A. Grin, A.P. Zent &
R. Quinn.
J. Geophys. Res. - Planets, 106, 23317-23326, October 2001
Using a validated general circulation model, we determine where and for how
long the surface pressure and surface temperature on Mars meet the
minimum requirements for the existence of liquid water in the present climate
system: pressures and temperatures above the triple point of water
but below the boiling point. We find that for pure waer, there are five "favorable"
regions where these requirements are satisfied ... in the plains of Amazonia, Arabia and Elysium, and in the Southern Hemisphere impact basins of Hellas and Argyre. The combined area of these regions represents 29% of the planet's surface area...These regions are remarkably well correlated with the location of Amazonian paleolakes mapped by Cabrol and Grin [2000]...obliquity variations may play a role. For brine solutions the favorable regions expand and could potentially include most of then
planet... Even rare events of liquid water formation would be significant
since they would dominate the chemistry of the soil and would have
biological implications as well. It is therefore worth re-assessing the
potential for liquid water formation on present day Mars, particularly in light of recent Mars Global Surveyor observations.

"For brine solutions the favorable regions expand and could potentially include most of then planet... Even rare events of liquid water formation would be significant since they would dominate the chemistry of the soil and would have biological implications as well."

The authors note that brine depresses the triple point pressure of water as well as the temperature, so possibilities for briny liquid water would include the high elevation locations in the southern
hemisphere. Interestingly they note it might also include the peaks in Tharsis.
This is notable because of recent evidence that there may be *active* glaciers in Tharsis:

Active Volcanism On Mars And The Search For Water
http://www.spacedaily.com/news/mars-volcano-01a1.html

Permafrost Springs on Earth and Mars
by Chris McKay
"There are two sets of perennial springs located on Axel Heiberg
Island that flow through 600 m of permafrost and these springs are not
associated with any volcanic heat sources. Located at nearly 80N these
are the most poleward springs known, and to our knowledge the only
example of cold springs in thick permafrost.
"Axel Heiberg Island is mostly bare ground, with less than 35% covered
by glaciers or ice caps. The average air temperature at the springs
sites is approximately -17C. The two springs both discharge a brine
with measured discharge temperatures that range from -2 to +6.5 C and
remain constant throughout the year despite air temperatures that fall
well below -40C. Flow rates are also constant with little variation."
http://chapters.marssociety.org/youth/mc/issue8/permafrost_springs.php3

Title: Martian Gullies and the Stability of Water in the Martian Environment
Authors: Thompson, J.; Sears, D. W. G.; Benoit, P. H.; Kareev, M. S.
Journal: 34th Annual Lunar and Planetary Science Conference, March 17-21, 2003, League City, Texas, abstract no.1035
http://adsabs.harvard.edu/cgi-bin/bib_query?2003LPI....34.1035T

The authors show by experiment simulating Mars environment and soil that flows can be formed under Mars conditions by liquid water.

Bob Clark