It seems like, being under ground, it would also be subject a higher than normal pressure, which would also help
From looking at the phase change chart[0], you don't really get into the "interesting" stuff as far as pressure goes until pretty deep (something like 9-10km, from looking at some sample number of pressure at various depths [1]). Given that they indicated in the article that this is under 1.5km of ice, I don't think that's deep enough to have pressure significantly change it, but would be happy to learn that I'm not correct in my reading of this :)
0 - https://physics.stackexchange.com/questions/60170/freezing-p... 1 - https://www.earthlearningidea.com/PDF/189_Pressure_rock.pdf - table on page 2
Pressure != compression, and water is otherwise sensitive to pressure. The boiling point of water varies by ambient air pressure, and in fact, the ambient air pressure on the surface of Mars is too low for liquid water, AFAIK; it boils away.
Also, see gmueckl's helpful comment: https://news.ycombinator.com/item?id=17610197
They mention Lake Vostok at the end of the article which is 4km deep but it's probably not directly comparable.
Now if I could get my hand on a phase diagram for water on which I could find that point (263K, 5.1MPa) I could tell you how close pure ice is to melting under these conditions.
https://upload.wikimedia.org/wikipedia/commons/0/08/Phase_di...