One might call this situation in the cartoon paranoia on the woman's part, but some of us would say we just work hard at being self-aware. :)
All joking aside, women are too often too concerned about their appearance and what others think of them. And are their own harshest critics about their bodies, and body image. The cartoon is an exaggeration, but judgments like this are quite common, unfortunately.
I'm not exactly sure why a pantyline is so bad—I guess the idea is to pretend one isn't wearing any?—but I have often been persuaded by labels to buy underwear that promise to help hide the line. I just hope the manufacturers have done their job and verified their claims, or else we're all at risk.