I think a lot of it has to do with the fact that guinea pig illnesses are more likely to be caused by bacteria than viruses. Whereas a lot of the illnesses that humans would just get over on their own are viral like a cold or flu, bacterial infections like strep or pneumonia often need treatment or they can prove fatal, even in humans. And a secondary consideration is that the guinea pig digestive system needs to be constantly in motion or secondary complications like gut stasis can set in, which can be fatal on their own. If a human is too sick to eat for a few days, they will lose weight but their digestive system will still be functioning at the end. If a guinea pig is too sick to eat for a few days, they will suffer a whole host of other problems as a result of their digestive system grinding to a halt.
I know my vet has told me a few times that guinea pigs simply don't deal well with illness in general. He says a lot of guinea pigs that are uncomfortable or ill will simply refuse food and water and will consequently have a bad outcome due to secondary factors. It's why he's so impressed with Sundae, who has had a lot of health issues (dental issues, a huge dental abscess all the way down to the bone, bladder stones, cystitis, etc.) And yet no matter what, she always gets up, walks around, and fights to eat and drink, even when her abscess first ripened up and she was so swollen that she couldn't open her mouth to pick up food and had to be syringed mushed up pellets. She still chewed and swallowed them and made attempts to eat normal food that she couldn't pick up due to swelling. He has said that most guinea pigs won't do that and that she must have the heart of a lion in the body of a guinea pig! LOL!