Not having a fit. The authors do not show that liquid water could not exist in localized spots even up to the present. Experts on extremophiles can tell you microbes can exist even in highly acidic environments or even when water is not present for thousands to millions of years in suspended form.
Also key is the fact that the authors reference a paper on Mars meteorites to support their position, but actually this paper reaches the opposite conclusion, that water existed intermittently at least to within 1 billion years ago, which includes the present Amazonian period:

ALTERATION ASSEMBLAGES IN MARTIAN METEORITES:
IMPLICATIONS FOR NEAR-SURFACE PROCESSES.
"Radiometric dating (K-Ar, Rb-Sr) of the secondary mineral assemblages in one of the nakhlites
(Lafayette) suggests that they formed between 0 and 670 Myr, and certainly long after the crystallisation of the host igneous rocks. Crystallisation of ALH84001 carbonate took place 0.5 Gyr after the parent rock. These age ranges and the other research on these assemblages suggest that environmental conditions conducive to near-surface liquid water have been present on Mars periodically over the last 1 Gyr. This fluid activity cannot have been continuous over geological time because in that case much more silicate alteration would have taken place in the meteorite parent rocks and the soluble salts would probably not have been preserved."
J. C. Bridges et al., Space Sci. Rev. 96, 365 (2001).
http://www.atmos.washington.edu/~davidc/papers_mine/Bridges_catling_2001.pdf

These meteorites show clays, carbonates and other aqueous minerals and the dating of these minerals show they stem from the Amazonian period on Mars.

Bob Clark