Well, they got denied by Försäkringskassan, “Swedish Social Insurance Agency”. Basically wouldn’t be able to get sick-pay, but that’s about it. Which is a bit weird, as nearly all first-time requests get approved, but of course it happens.
So it’s not really the same thing as American insurance denying; they’re still able to seek care, just that the suggested treatment for burnout (pause from working) wouldn’t be economically comfortable if Försäkringskassan denies their sick-pay.