This observation is correct, but with a twist you can see how it may not be so:
Arya caused her to rise from death. The part of being found by Beric and re-animated by the power of R'Hillor - is that all there is to it ?
Mourneblade states quite correctly that Arya is a special case - magic, divine will, or whatever you'd call it, does seem to play a role in her story. She may have a sort of power that we do not quite see, that works at strange angles to the story.
"Rise" she thought. "Rise and eat and run with us."
The Ghost of High heart saw this as well. She thought it was Beric who smelled of death and grief, but then realized this prophecy was tied to Arya.
So many lives given at Harrenhal, so perhaps the Red God owed her ?
What is Lady Stoneheart if not a revenant forever trapped in Catelyn's last moments of grief and rage ?
So, why not Arya? She brings the gift of death, and in this case, it would be one which ends her mother's living hell.
As much as her un-mother's quest for vengeance is something she can best relate to, she also knows the wellspring of emotional horror that it comes from. She may be willing to suffer those burdens herself, but would she want her mother to live in that state, eternally ?
Perhaps this is a way it will lead her to a greater understanding of "the gift" as a gift.