How do some humans seemingly naturally have positive or mitigated appraisal of stressful events?
The interactions among several factors probably account for variability in reactivity to stressful events, including genetics, epigenetics, early life experience, and culture (e.g., Alexander et al., 2009; Boyce &amp; Ellis, 2005; Francis, Frances, Liu, &amp; Meaney, 2006; Gunthert et al., 2007; Meaney, 2001).  And individual differences are observable at multiple levels of analysis, including behavior, physiology, and brain structure and function.  

On the one hand, there is a huge literature on the development of emotion regulation in children (e.g., positive appraisal of stressful events).  For example, there are models charting the complex influence of the family on emotion regulation development, where parenting practices interact with child characteristics to influence emotion regulation success and strategy use (Morris et al., 2007):



Positive (re)appraisal requires good cognitive control and working memory (McRae et al., 2012), which is associated with functional and structural integrity of cortical areas, most notably prefrontal cortex (Goldsmith, Pollack, &amp; Davidson, 2008; Levesque et al., 2004; Lewis &amp; Stieben, 2004; McRae et al., 2012).  And the ability of PFC to dampen negative affect seems to be mediated by functional connectivity with subcortical areas, notably bilateral amygdala (Banks et al., 2007; Buhle et al., 2014; Wager et al., 2008).  



Positive reappraisal also benefits from practice, which forms part of the basis of cognitive-behavioral therapy (Beck, 2011; Goldin et al., 2012; Goldin et al., 2013).  

Additionally, there is emerging evidence that genes (and gene-environment interactions) are related to emotion regulation strategy use and effectiveness (e.g., 5-HTT, OXTR; Canli &amp; Lesch, 2007; Hariri &amp; Holmes, 2006; Kim et al., 2011).  So genetic factors may promote resilience even in stressful environments. 

Conclusion

So as you can see, there is a large host of factors that contribute to one's tendency to appraise (negatively or positively) a stressful situation. And indeed, you may see large within-person variability in the tendency to make positive appraisals, especially as the context changes (Aldao &amp; Nolen-Hoeksema, 2012). Not to mention, positive appraisal may not always be a beneficial way to mitigate stress, and may instead sometimes be harmful or ineffective (Troy, Shallcross, &amp; Mauss, 2013).