It's really about dismissal of someone's feelings and not recognizing it.

Someone having just a negative moment needs compassion, not a positive spin.

Someone comfortable in negative thoughts needs compassion and a positive spin.

The difference here is in the term "silver lining." If you're looking for the silver lining, it's essentially belittling the pain someone is going through as it roughly translates to "please feel better so we can go back to normal." The only person allowed to observe the silver lining is the person feeling upset.

For the people that find comfort in a negative mindset, yeah, you basically have to contend with their glass-half-empty-will-run-out worldview using a glass-half-full-could-be-fuller view and actually show them their worries are misplaced. No one wants to be a glass-half-empty thinker, it's a coping mechanism because they're just tired of feeling like all they ever do is lose and expecting and accepting the next loss ahead of time softens the blow.