It was adapted for the situation from No True Scotsman, admittedly partially because I grew up Christian and have heard this sentiment before (a close relative of the pervasive Prosperity Gospel), but mainly because we are discussing spirituality. I am calling you a Christian in this instance no more than I would have been calling you a Scotsman with the traditional wording. Regardless, the fallacy would be there even if I did mistakenly pin you as a Christian.

Suffice it to say, I find it cruel and absurd to believe that someone suffering from depression must not really have a relationship with their god, and I urge you to reconsider your beliefs in this matter.