Nor can you just be work sick. Work sick is totally different from sick sick. Sick sick is physical. Work sick is motivational. The only people who don't understand the difference between sick sick and work sick are bosses.
Bosses think all sick is work sick.
So if you call in sick, even if you are under the care of a mortician, the boss thinks you are work sick. But if you come in sick, the boss thinks you are a trouper, even though what you really are is a carrier. If the logic of this escapes you, understand that this is among the reasons you sit in the open-plan section and not in the corner office. The only people who are more suspicious of sickness than bosses are spouses. It is a trap.