Timing
The crucial issue is one of timing and temperatures.
Nothing stops water ice (either thin seasonal frosts or deeper permafrost) from behaving in this fashion, but those are the papers of Costard et al. and Lee at al.
What I have done is looked at the time when flow events occur and show that the gullies are frosted-in with dry ice at the time.
The gullies do not appear to flow later in the season when liquid water mught be possible.
There are also plausible arguments that the volume of annual water ice is negligible and the nett erosion of buried ice by summer melting is also negligible, but these are not binding.