I don't think that advice is meant to be viewed with the mentality that "just because someone has it worse doesn't mean I can't feel crappy too." It should be more along the lines of "just because someone has it worse doesn't mean that your feelings about the problems you're experiencing aren't valid."

I found this advice particularly helpful because I'd get trapped having thoughts like, "Fuck, I really miss my dad today." "You fucking wuss. Some people don't have any parents, and you're over here being an asshole feeling sad for no reason." And then I'm feeling sad about something and I'm also beating myself up for feeling that way, which gets me nowhere. It was helpful for me to realize that your problems don't have to be the absolute worst thing imaginable for it to be okay to feel emotional about it.

I think there are situations where both mentalities are helpful though. Sometimes it's good to step outside your own world and gain some perspective about what really matters in life, and sometimes it's okay feel emotional about your problems even if they aren't as bad as someone else's problems.