In your example, you are describing social stress. I think you are right that social stress is mainly driven by reflective processes. Also, social stress without reflective processes sounds quite implausible to me.
However, we should keep in mind that stress can come from various sources, some of which are non-social. For example, one common way to induce stress in psychological experiments is to use a physiological (as opposed to a psychosocial) stressor. In the classic cold pressor test, participants are instructed to put their hand into ice water. This starts a stress reaction, as measureable for example by increases in cortisol. I think it's pretty safe to say that reflective processes are not the driving factor here.
For a review on different methods to induce stress in the lab, see for example: